Appeal from an order of the Supreme Court, Ontario County (William F. Kocher, A.J.), entered June 22, 2012 in a proceeding pursuant to CPLR article 75. The order denied the petition to stay arbitration and granted respondent’s cross motion to compel arbitration.
It is hereby ordered that the order so appealed from is unanimously affirmed without costs.
Memorandum: Petitioners commenced this proceeding to stay arbitration (see CPLR 7503 [b]), and respondent “cross-moved” to compel arbitration with respect to grievances allegedly involving a provision of the parties’ collective bargaining agreement (CBA) (see CPLR 7503 [a]). Pursuant to the CBA, disputes over the meaning or application of that agreement were required to *1464be submitted first through a grievance process, but could thereafter be submitted to arbitration if the employee was “not satisfied” with the result obtained through that process. Respondent filed grievances on behalf of two correction officers whose request for a shift exchange was denied. Respondent asserted that the denial “[violated or [ijnvolved” section 3.11 of the CBA, which provides that “time exchanged between employees shall not be done if it results in a requirement. . . that overtime be paid,” and respondent requested that the shift exchanges be allowed. The grievances also involved the application of a Shift Swapping Policy, which was not contained in the CBA, between respondent and petitioner Ontario County that outlined the specific procedures an employee must follow when exchanging a shift with a fellow employee. The Shift Swapping Policy states with respect to shift swapping on holidays that the person working the holiday receives the holiday pay “[t]o be consistent with contract language.” The grievances were denied, and respondent informed petitioners of its intent to seek arbitration. As noted, petitioners filed a petition to stay arbitration, and respondent “cross-moved” to compel arbitration. Supreme Court denied the petition and granted the cross motion, and we affirm.
“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” (Matter of City of Johnstown [Johnstown Police Benevolent Assn.], 99 NY2d 273, 278 [2002]; see Matter of Board of Educ. of Watertown City School Dist. [Watertown Educ. Assn.], 93 NY2d 132, 137-142 [1999]). Here, the parties do not challenge the lawfulness of arbitrating the instant dispute and, instead, petitioners contend that there is no valid agreement to arbitrate the grievances at issue inasmuch as the CBA did not contemplate shift exchanges. We reject that contention.
In determining whether the parties agreed to arbitrate the dispute at issue, “[o]ur review ... is limited to the language of the grievance and the demand for arbitration, as well as to the reasonable inferences that may be drawn therefrom” (Matter of Niagara Frontier Transp. Auth. v Niagara Frontier Transp. Auth. Superior Officers Assn., 71 AD3d 1389, 1390 [2010], lv denied 14 NY3d 712 [2010]). “Where, as here, there is a broad arbitration clause and a ‘reasonable relationship’ between the subject matter of the dispute and the general subject matter of the parties’ [CBA], the court ‘should rule the matter arbitrable, and the arbitrator will then make a more exacting interpretation of the precise scope of the substantive provisions of the *1465[CBA], and whether the subject matter of the dispute fits within them’ ” (Matter of Van Scoy [Holder], 265 AD2d 806, 807-808 [1999], quoting Matter of Board of Educ. of Watertown City School Dist., 93 NY2d at 143; see Matter of Town of Cheektowaga [Cheektowaga Police Club, Inc.], 59 AD3d 993, 994 [2009]). We therefore conclude that the court properly determined that the parties agreed to arbitrate the instant dispute. In light of our determination, we do not address petitioners’ remaining contentions. Present—Centra, J.P., Fahey, Garni, Sconiers and Martoche, JJ.