This appeal returns to this court on remand from our Supreme Court; State v. Nokes, 239 Conn. 926, 685 A.2d 22 (1996); so that we may reconsider our decision affirming the judgment of the trial court in light of the Supreme Court’s recent decision in State v. Gerardi, 237 Conn. 348, 677 A.2d 937 (1996).
The facts of the present case are set forth in State v. Nokes, 42 Conn. App. 10, 11-13, 678 A.2d 510 (1996), and do not warrant repetition here. The dispositive question was “whether the trial court’s instruction on the rebuttable presumption in General Statutes (Rev. to 1995) § 14-227a (c) impermissibly shifted the burden of proof on an essential element of the offense of operating a motor vehicle while under the influence of intoxicating liquor in violation of General Statutes (Rev. to 1995) § 14-227a (a).”1 Id., 10-11. We held that although § 14-227a (c) specifically creates a rebuttable *42presumption,2 the jury charge “allowed the jury to make a permissive inference in that it could consider the [chemical analysis] test results and attach whatever weight it chose to them. The charge did not impermissibly allow the state to use an evidentiary presumption to relieve itself of its burden of persuasion beyond a reasonable doubt of every essential element of a crime.” Id., 12.
State v. Gerardi, supra, 237 Conn. 348, concerned the rebuttable presumptions contained in General Statutes § 53-202 (e) and (g). Subsection (e) provides: “The presence of a machine gun in any room, boat or vehicle shall be presumptive evidence of the possession or use of the machine gun by each person occupying such room, boat or vehicle.” Subsection (g) provides in relevant part: “Any person who fails to register any gun as *43required hereby shall be presumed to possess the same for an offensive or aggressive purpose. ...” Gerardi was charged with possession of a machine gun for an offensive or aggressive purpose in violation of § 53-202. He was sitting in the front passenger seat of a car that was seen leaving the scene after the sound of several rapidly fired gunshots. Police officers found shell casings behind the defendant’s seat and his window was open. Police later found, at the side of the road, a machine gun and magazine from which the casings found in the vehicle had been fired. The trial court had instructed the jury that, “pursuant to § 53-202, the presence of a machine gun in any vehicle shall be presumptive evidence of possession or use of the gun, and that the failure to register the gun or the presence of any empty or loaded projectiles of any caliber, which have been or are susceptible of use in the machine gun, is presumptive evidence that the gun was possessed for an offensive or aggressive purpose. . . . ‘[Presumptive evidence is defined as evidence which must be received and treated as true and sufficient until rebutted by other testimony.’ ” Id., 355. The Supreme Court held that the instructions did violate the due process clause and that they were not harmless beyond a reasonable doubt.
The only difference between the Gerardi charge and the Nokes charge is that the Gerardi charge used the term “presumptive evidence” and defined the term as evidence that must be treated as true and sufficient to prove the element of the crime to which it pertains until the presumptive evidence is rebutted by other testimony. Although the Gerardi charge did not specifically instruct the jury that it was the defendant’s burden to rebut the presumptive evidence, that was clearly the implication of the words used. The Nokes charge did not inform the juiy that a presumption was to be taken as sufficient proof by itself of an element of the crime, *44but it did require the presumptions to be “overcome by the defendant through the introduction of other evidence” and allowed the jury to decide whether the defendant’s evidence “successfully rebutted the presumptions.”
The state has asked us to clarify our original opinion and state that the trial court’s jury charge on the presumption in § 14-227a (c) was tantamount to an instruction that the presumption was a permissive inference. We cannot do this because we cannot change the words of the trial court. The trial court cast its instruction in terms of rebuttable presumptions. Pursuant to Gerardi, we must conclude that the trial court’s instructions to the jury in the present case were improper. The question remains, however, whether the instruction was harmless beyond a reasonable doubt.
To pass constitutional muster, a presumption must be cast as a “permissive inference [that] suggests to the jury a possible conclusion to be drawn if the State proves predicate facts, but does not require the jury to draw that conclusion. . . .A permissive inference does not reheve the State of its burden of persuasion because it still requires the State to convince the jury that the suggested conclusion should be inferred based on the predicate facts proved.” Francis v. Franklin, 471 U.S. 307, 314, 105 S. Ct. 1965, 85 L. Ed. 2d 344 (1985).
Instructions relating to § 14-227a (c) should fulfill the legislature’s intent that a jury may infer a defendant’s blood alcohol content at the time of the offense under appropriate factual circumstances. “Accordingly, we construe . . . statutory inferences as permissive inferences that a jury may draw under appropriate circumstances in which such an inference is rational or reasonable.” State v. Gerardi, supra, 237 Conn. 360.
“If . . . other facts or circumstances are introduced and the totality of the evidence could reasonably and logically support the inference, then the jury may be *45instructed that it may draw such a permissive inference. . . . [T]he jury must be instructed that it may infer facts only upon finding sufficient predicate statutory and nonstatutory facts and circumstances that are rationally connected with the ultimate facts inferred.” Id., 361. Here, the ultimate fact to be proven is that the defendant’s blood alcohol content at the time of the offense was 0.10 percent or greater. According to the statute, this fact may be “presumed” if the jury finds that after testing according to statutory requirements, the test results show that the defendant’s blood alcohol content was 0.10 percent or greater. To find this ultimate fact, the jury must first determine if the statutory guidelines were followed. The test must have been performed by a proper person, the device used must be shown to have been working properly, and the test must have been performed within the proper time frame.
If a “permissive presumption,” namely, a finding of a blood alcohol content greater than 0.10 percent, “leaves the trier of fact free to credit or reject the inference and does not shift the burden of proof, it affects the application of the beyond a reasonable doubt standard only if, under the facts of the case, there is no rational way the trier could make the connection permitted by the inference. . . . [I]n that situation [the] risk [is] that an explanation of the permissible inference to a jury, or its use by a jury, has caused the presumptively rational factfinder to make an erroneous factual determination.” (Internal quotation marks omitted.) State v. Gerardi, supra, 237 Conn. 358, quoting Ulster County Court v. Allen, 442 U.S. 140, 157, 99 S. Ct. 2213, 60 L. Ed. 2d 777 (1979).
In Gerardi, the court concluded that the legislature could not have intended that the jury be required to infer that a defendant possessed a machine gun for an offensive or aggressive purpose from the mere fact that the gun was unregistered or that the jury was required *46to infer that all the occupants of a vehicle possess a machine gun simply because it is located in that car. The legislature could have intended only that a jury may infer possession under appropriate factual circumstances.
In the present case, unlike in Gerardi, there is a rational connection between the subsidiary facts and the ultimate fact. The conclusion that the ultimate fact that the blood alcohol content was 0.10 percent can be inferred by the proof of the subsidiary facts. Unlike in Gerardi, there is no other charge in Nokes of which the defendant was found not guilty that would cast doubt on the finding of guilty of the first charge. The charge of which Gerardi was found not guilty implicated possession, an element of the crime for which he was found guilty, thereby casting doubt on the ultimate finding by the jury of the defendant’s guilt of the fust charge of possession. The jury, therefore, could have used the presumption of possession to find the defendant guilty.
The trial court in the present case charged the jury that to find the defendant guilty it must find that the state proved beyond a reasonable doubt that the defendant’s blood alcohol content was 0.10 percent or more at the time of the incident. The trial court went on to explain that “ [i]f you find that the results of the chemical analysis test are above twelve hundredths of one percent, and that the test was commenced within two hours of the time of operation, then you can find that the ratio of alcohol in the defendant’s blood was in excess of the legal limit of ten hundredths of one percent at the time of operation.”
The officer who arrested Nokes had testified that he was certified to operate the testing equipment, and he also produced the log book that showed that the equipment was working properly at the time. The jury could have concluded from the evidence before it that the *47test was performed properly by a qualified person, that the device was working properly, and that the test was performed within the proper time frame. From these subsidiary facts, it ultimately could have concluded, beyond a reasonable doubt, that the defendant’s blood alcohol content exceeded the statutory requirement of 0.10 percent at the time of testing.
The fact that the trial court instructed the jury that the “presumptions can be overcome by the defendant through the introduction of other evidence,” does not necessarily mean that the jury instructions could not be proved harmless beyond a reasonable doubt. The defendant introduced evidence, through an expert, that the testing for blood alcohol content by a breath test is not conclusive evidence of a person’s earlier blood alcohol content. This evidence was not offered to rebut the “presumption” of § 14-227a, but rather to cast doubt on the reliability of the testing procedure and results. The jury opted to believe in the reliability of the testing results to infer that an element of the crime was proved beyond a reasonable doubt.
We conclude that the state has proved that the court’s instruction was harmless beyond a reasonable doubt.
The judgment is affirmed.
In this opinion the other judges concurred.
The relevant part of the charge to the jury was as follows: “In any criminal prosecution for driving a vehicle while under the influence of, or affected by the use of, intoxicating liquor, the amount of alcohol in the defendant’s blood at the time alleged is shown by chemical analysis of the defendant’s blood, urine, breath or other bodily substance, shall give rise to the following presumptions: If there was at that time ten hundredths of one percent or more by weight of alcohol in the defendant’s blood, it shall be presumed that the defendant was under the influence of intoxicating liquor. If you find that the result s of the chemical analysis test are above twelve hundredths of one percent, and that the test was commenced within two hours of the time of operation, then you can find that the ratio of alcohol in the defendant’s blood was in excess of the legal limit of ten hundredths of one percent at the time of operation. These presumptions are rebuttable presumptions. These presumptions can be overcome by the defendant through the introduction of other evidence. You will recall that the defense introduced the testimony of [Brian] Pape, an expert in the field of toxicology. It is for you to decide whether or not to believe all or any part of his testimony, and whether or not his testimony successfully rebutted the presumptions.” (Emphasis added.) See State v. Nokes, supra, 42 Conn. App. 11-12.
General Statutes (Rev. to 1995) § 14-227a (c) provides in pertinent part: “Except as provided in subsection (d) of this section, in any criminal prosecution for violation of subsection (a) or (b) of this section, evidence respecting the amount of alcohol or drug in the defendant’s blood or urine at the time of the alleged offense, as shown by a chemical analysis of the defendant’s breath, blood or urine shall be admissible and competent provided ... (3) the test was performed by or at the direction of a police officer according to methods and with equipment approved by the department of public health and addiction services and was performed by aperson certified or recertified for such purpose by said department or recertified by persons certified as instructors by the commissioner of public health and addiction services.
. . . (4) the device used for such test was checked for accuracy immediately before and after such test was performed by a person certified by the department of public health and addiction services; (5) an additional chemical test of the same type was performed at least thirty minutes after the initial test was performed, provided however the results of the initial test shall not be inadmissible under this subsection if reasonable efforts were made to have such additional test performed in accordance with the conditions set forth in this subsection and such additional test was not performed or was not performed within a reasonable time, or the results of such additional test are not admissible for failure to meet a condition set forth in this subsection; and (6) evidence is presented that the test was commenced within two hours of operation. In any prosecution under this section it shall be a rebuttable presumption that the results of such chemical analysis establish the ratio of alcohol in the blood of the defendant at the time of the alleged offense . . . .” (Emphasis added.)