OPINION OF THE COURT
Rosenblatt, J.In these appeals, Police Benevolent Associations (PBAs) in the Cities of Johnstown and Schenectady sought arbitration of grievances concerning the calculation of certain employees’ retirement benefits pursuant to the formula contained in Retirement and Social Security Law § 302 (9) (d). Both cases present the same question: whether the grievances are arbitrable. We conclude that they are, and therefore affirm the Appellate Division orders dismissing the Cities’ petitions to stay the arbitrations.
I.
In December 1998 and April 1999, the PBAs and the Cities of Johnstown and Schenectady, respectively, signed the collective bargaining agreements (CBAs) at issue. The agreements contain the terms and conditions of employment for police officers, and were negotiated and signed by the municipalities and the PBAs. Under each CBA, retirement benefits were to be computed using the definition of “Final Average Salary” in Retirement and Social Security Law § 302 (9) (d).1 When the parties signed the CBAs, the statute provided that retirement benefits for Tier I police and fire employees could be based on an employee’s average monthly salary for the 12 months immediately preceding retirement. Tier I employees were statutorily defined as “employees of a participating employer who were such employees on or before June thirtieth, nineteen *277hundred seventy-three” (former Retirement and Social Security Law § 302 [9] [d]).
In November 1999, the Legislature amended Retirement and Social Security Law § 302 (9) (d). Under the amended statute, the Legislature extended the 12-month calculation formula to non-Tier I employees (see L 1999, ch 638, § 1). There was (and remains) no obligation on the part of employers, however, to provide this benefit. Instead, Retirement and Social Security Law § 443 (f-1) states that employee demands for the section 302 (9) (d) retirement benefits formula shall not be subject to compulsory interest arbitration (see Retirement and Social Security Law § 443 [f-1] [citing Civil Service Law § 209 (4) (b)- (c)]).
After the amendment to section 302 (9) (d), the PBAs argued to the Cities that the CBAs’ reference to section 302 (9) (d) made all members of the bargaining unit, specifically Tier II employees, eligible for those benefits. When the Cities declined to provide the section 302 (9) (d) benefits to Tier II employees, the PBAs issued a demand for arbitration, relying on the broad arbitration clauses of the CBAs.2
The Cities then filed CPLR article 75 petitions to stay the arbitrations, and Supreme Court, in each case, granted the stay. In Johnstown, the court reasoned that the City and the PBA did not intend to provide the retirement benefits to Tier II employees, given that when the agreements were signed, the City was not legally permitted to provide benefits to anyone other than Tier I employees. In Schenectady, the court held that Retirement and Social Security Law § 443 (f-1) prohibited arbitration of disputes concerning the allocation of these retirement benefits to Tier II employees.
In both cases, the Appellate Division reversed and dismissed the petitions. Finding a “reasonable relationship” between the subject matter of the CBAs and the PBAs’ grievances, the Court found the matters arbitrable (see Matter of City of Johnstown [Johnstown Police Benevolent Assn.], 289 AD2d 832, 833 [2001]; Matter of City of Schenectady [Schenectady Police Benevolent Assn.], 289 AD2d 814, 815-816 [2001]). We affirm.
*278II.
A grievance may be submitted to arbitration only where the parties agree to arbitrate that kind of dispute, and where it is lawful for them to do so. In determining whether a grievance is arbitrable, we therefore follow the two-part test enunciated in Matter of Acting Supt. of Schools of Liverpool Cent. School Dist. (United Liverpool Faculty Assn.) (42 NY2d 509 [1977] [Liverpool]) and Matter of Board of Educ. of Watertown City School Dist. (Watertown Educ. Assn.) (93 NY2d 132, 143 [1999] [Watertown]). We first ask whether there is any statutory, constitutional or public policy prohibition against arbitration of the grievance (see Liverpool, 42 NY2d at 513). This is the “may-they-arbitrate” prong. If there is no prohibition against arbitrating, we then examine the CBA to determine if the parties have agreed to arbitrate the dispute at issue (see Water-town, 93 NY2d at 140; Liverpool, 42 NY2d at 513-514). This is the “did-they-agree-to-arbitrate” prong.
A.
The Cities contend that this case fails both prongs. As to the “may-they-arbitrate” prong, they, and the dissent, assert that when the parties signed the CBAs it would have been illegal to provide the retirement benefits of Retirement and Social Security Law § 302 (9) (d) to Tier II employees. Their argument misses the point. The relevant inquiry is not whether the benefits may be lawfully provided,3 but whether law or public policy bars arbitration of the grievances.
As to that, the Cities cite Retirement and Social Security Law § 443 (f-1). That statute, however, does not control whether the grievance is arbitrable. True, pursuant to section 443 (f-1), the allocation of section 302 (9) (d) benefits is exclusively within the prerogative of the employer, and Tier II employees may not seek redress through interest arbitration when their employers refuse to give them that benefit during collective bargaining. The PBAs here, however, are not arguing that their Tier II members should be given the retirement *279benefits. Instead, they are arguing, in essence, that the preexisting CBA already gave them the benefits. In sum, the dispute at the heart of this case is not the negotiation of a provision of a CBA (which, pursuant to section 443 [f-1], may not go to arbitration), but the interpretation of a CBA provision (which section 443 [f-1] does not address). We conclude that there is no statutory, constitutional or public policy bar preventing the parties from agreeing that an arbitrator will decide whether they intended in these clauses to extend benefits to Tier II employees if and when it became lawful for municipalities to do so.
B.
In arguing that the case fails Liverpool-Watertown prong two, the Cities assert that the parties did not intend, and the CBAs do not evince any intent, to arbitrate this dispute. According to the Cities, they could not have intended to arbitrate whether Tier II employees were entitled to these retirement benefits because, under the law existing at the signing of the CBAs, Tier II employees were precluded from receiving those benefits. Again, however, by raising the merits of the grievance, the Cities frame the issue improperly. The appropriate inquiry is whether the parties agreed to have arbitrators decide the proper interpretation of the CBAs’ retirement benefits provisions.
We have steadfastly maintained a distinction between the merits of grievances and the threshold question of whether courts or arbitrators have the authority to decide the merits. In Watertown we stressed the importance of keeping the inquiries separate. “Even an apparent weakness of the claimed grievance is not a factor in the court’s threshold determination. It is the arbitrator who weighs the merits of the claim” (Water-town, 93 NY2d at 142). CPLR 7501 also directs that, when deciding whether a dispute is arbitrable, “the court shall not consider whether the claim with respect to which arbitration is sought is tenable, or otherwise pass upon the merits of the dispute.”
Our task, as we stated in Watertown and as the Appellate Division correctly held, is merely to “determine whether there is a reasonable relationship between the subject matter of the dispute and the general subject matter of the CBA” (Water-town, 93 NY2d at 143). The CBAs provide that the PBAs may request arbitration for unresolved grievances. There is no exception in the CBAs for grievances concerning retirement *280benefits, either generally or for Tier II employees. Therefore, we conclude that the reasonable relationship test is readily met, and this dispute is arbitrable.
Accordingly, in each proceeding, the order of the Appellate Division should be affirmed, with costs.
. The Johnstown CBA states that retirement benefits should be calculated “pursuant to Section 384 subdivision d of the New York Retirement and Social Security Law. (final 12 month average salary plan).” That section, however, does not prescribe a method of calculating retirement benefits. The City of Johnstown agrees with the PBA that the CBA should be interpreted to refer to section 302 (9) (d). The City notes that section 302 (9) (d) benefits were automatically conferred to Tier I police officers when the benefits were given to Tier I firefighters in a separate CBA (see Brief of City of Johnstown at 3 n 1).
. The Johnstown agreement states that “[i]n the case of unresolved grievances, the [PBA] may request arbitration in accordance with the rules of the Public Employment Relations Board relating to arbitration.” The Schenectady agreement states that “[a]ny unresolved grievance having been processed fully through the last step of the grievance procedure may be submitted to arbitration by either party * * Both agreements define “grievance” to include disputes over the interpretation or application of the CBAs.
. Even here, however, the Cities’ argument is dubious. The Cities conceded at oral argument, correctly, that there would be no statutory, constitutional or public policy prohibition against awarding benefits to Tier II employees if the CBAs had explicitly said that they would incorporate any future changes made to Retirement and Social Security Law § 302 (9) (d). Accordingly, after the 1999 amendment to Retirement and Social Security Law § 302 (9) (d), there is no prohibition against calculating Tier II retirement benefits by using the 12-month average salary formula.