Mikel W. Houston appeals the denial of his petition for a writ of habeas corpus brought under 28 U.S.C. § 2254 (1988). Houston is serving a life sentence for rape. He claims his counsel was ineffective in failing to secure a stipulation to admit certain polygraph test results into evidence at trial and failing to pursue the issue on appeal. He also contends that his counsel should have raised the ineffective assistance issue on appeal. The district court1 concluded that: (1) an objection to the prosecution’s refusal to stipulate to the test results would have been futile in light of Arkansas’ law on the admission of polygraph test results; and Houston’s asserted error was unreviewable because it did not infringe upon his constitutional protections, *828and was not so prejudicial as to deny due process. We affirm the district court’s order denying the petition.2
A jury convicted Houston of raping his twelve year-old daughter LaDonna by deviate sexual activity. Because he was a habitual offender, the jury sentenced him to life imprisonment. The Arkansas Supreme Court affirmed the conviction on direct appeal. Houston v. State, 293 Ark. 492, 739 S.W.2d 154 (1987). Houston filed a petition for post-conviction relief under Arkansas Rule of Criminal Procedure 37 with the Arkansas Supreme Court, specifically asserting ineffective assistance of counsel. Houston claimed that the prosecution and defense preliminarily agreed to admit his polygraph test results at trial, but that after he took the tests, the prosecution reneged on its agreement and defense counsel made no objection.3 Houston filed with the Arkansas Supreme Court a copy of the polygraph examiner’s report indicating that he was truthful during the tests in denying the sexual contact with his daughter.
The Arkansas Supreme Court held that polygraph tests are admissible only if both parties agree in writing to the admission. Houston v. State, No. CR 87-85, slip op. at 1, 1988 WL 14162 (Ark. Feb. 22, 1988). There was no evidence that the prosecution had made such a written agreement. Accordingly, the test results were not admissible, making an objection by the defense futile. Id. The court stated Houston had not proven that his trial would have turned out differently had the test results been admitted. Id. at 2. The court could not conclude that there was a reasonable probability that the test results would have so bolstered Houston’s credibility as to persuade the jury to acquit him. Id. The court also rejected arguments that Houston’s counsel failed to file an adequate appellate brief, as Houston had not shown a meritorious issue omitted in his appeal. Id.
Houston then filed this habeas petition in the United States District Court, claiming, among other issues, ineffectiveness of counsel both at trial and on appeal. The district court agreed with the Arkansas Supreme Court that an objection to the prosecution’s refusal to stipulate to the admission of the polygraph test results would have been futile absent an existing written stipulation. Houston v. Lockhart, No. PB-C-88-294, slip op. at 6 (E.D.Ark. Aug. 28, 1990). The district court also rejected Houston’s claim that his counsel failed to file an adequate appellate brief. Id. The district court concluded that Houston’s counsel was not ineffective. Id. at 3-6. After disposing of other claims Houston has not raised on this appeal, the district court denied his petition. Id. at 9.
Houston argues that his counsel’s actions constitute ineffective assistance under the standards of Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). He asserts that the very fact that his trial counsel did not stipulate to the admission of the polygraph test results demonstrates their ineffectiveness, and severely affected his chances of acquittal. Houston also points to his counsel’s failure to raise the issue on appeal. He further claims that his counsel failed to raise the ineffective assistance claim on appeal because they continued to represent him at that proceeding. The ultimate conclusion as to whether Houston was deprived of effective assistance of counsel is a question of law that we review de novo.4 See Kellogg v. Scurr, 741 F.2d 1099, 1101 (8th Cir.1984).
A defendant claiming a violation of the sixth amendment right to effective assistance of counsel must show that: (1) *829counsel's representation fell below an objective standard of reasonableness; and (2) a reasonable probability exists that counsel’s error prejudiced the defendant. Strickland, 466 U.S. at 687-95, 104 S.Ct. at 2064-69; Spillers v. Lockhart, 802 F.2d 1007, 1009 (8th Cir.1986).
Under the first Strickland standard, we consider whether Houston’s counsel acted unreasonably in failing to secure a stipulation to admit his polygraph test results into evidence. Arkansas law requires a written stipulation of both parties before polygraph tests are admissible. Foster v. State, 285 Ark. 363, 369-70, 687 S.W.2d 829, 832 (1985), cert. denied, 482 U.S. 929, 107 S.Ct. 3213, 96 L.Ed.2d 700 (1987); see also Ark. Code Ann. § 12-12-704 (Michie 1987) (polygraph test results are generally not admissible in Arkansas courts). The prosecution was under no obligation to make a written stipulation regardless of any alleged oral agreement it may have made before Houston took the polygraph tests. We agree with the Arkansas Supreme Court and the district court that an objection would have been fruitless in the face of the prosecution’s refusal to make a stipulation.
Having determined that Houston’s counsel’s representation did not fall below an objective standard of reasonableness, we need not consider the second Strickland issue of whether a reasonable probability exists that Houston was prejudiced by the alleged error. We are convinced, however, that there is no reasonable probability that the admission of the results would have affected the outcome of Houston’s trial. We cannot say there is a reasonable likelihood that the polygraph test results would have so bolstered Houston’s credibility as to override LaDonna Houston’s testimony of what occurred.
Houston argues that his counsel should have raised the polygraph test results issue on appeal. He also claims that counsel did not raise the issue of their own incompetence on appeal because “it is not reasonable to expect trial counsel to assert their own shortcoming in this case.” As we have stated, the law of both this circuit and Arkansas would have made it fruitless for counsel to object to the court’s refusal to allow Houston’s polygraph test results into evidence. Raising the issue on appeal would have been equally unavailing. Furthermore, Houston’s argument that his counsel should have raised the ineffective assistance claim on appeal is without merit, as the proper place to raise such a claim is in a Rule 37 petition, Carrier v. State, 278 Ark. 542, 647 S.W.2d 449, 450 (1983). This Houston did, and the Arkansas Supreme Court decided the issue adversely to Houston on the merits. We see no ineffectiveness in failing to raise this issue on direct appeal.
We affirm the district court’s judgment denying the writ.
. The Honorable Henry Woods, United States District Judge for the Eastern District of Arkansas.
. Houston has not raised a due process argument on appeal and we do not reach it, but it is abundantly clear that the district court did not err in its handling of this issue.
. Houston's rule 37 motion filed with the Arkansas court asserts only an agreement between his attorney and the prosecutor with respect to the polygraph results, but his petition filed with the district court adds the statement that the judge was present and participated in the verbal agreement.
.Houston assumes that the district court held that he procedurally defaulted on his claim because his counsel did not raise it on appeal in state court. To the contrary, the district court ruled on the merits of the claim, Houston v. Lockhart, slip op. at 3-6.