It is hereby ordered that the order so appealed from is unanimously reversed on the law without costs, the petition is denied, and the cross petition is granted.
Memorandum: Respondent appeals from an order granting petitioner’s CPLR article 75 petition for a permanent stay of arbitration and denying respondent’s cross petition to compel arbitration. We reverse.
Respondent, which represents employees holding the position of captain with petitioner, demanded arbitration concerning the promotion of a firefighter to acting captain to cover an alleged vacancy in the position of captain. The sole question presented on this appeal is whether the parties have “agreed to arbitrate the dispute at issue” pursuant to their collective bargaining agreement (CBA) (Matter of City of Johnstown [Johnstown Police Benevolent Assn.], 99 NY2d 273, 278 [2002]; see Matter of Town of Cheektowaga [Cheektowaga Police Club, Inc.], 59 AD3d 993, 994 [2009]; Matter of City of Watertown v Watertown Firefighters, Local 191, 6 AD3d 1095 [2004]). Our review of that question 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 (see generally Matter of Board of Educ. of Schenectady City School Dist. [Schenectady Fedn. of Teachers], 61 AD3d 1175 [2009]; Matter of City of Ithaca [Civil Serv. Empls. Assn., Inc.], 25 AD3d 859, 860-861 [2006], lv denied 6 NY3d 712 [2006]; Matter of Smith v Andrews, 122 AD2d 310, 313-314 [1986], lv denied 69 NY2d 604 [1987]).
“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 [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. [Watertown Educ. Assn.], 93 NY2d 132, 143 [1999]; see Town of Cheektowaga, 59 AD3d at 994).
Petitioner’s reliance on Matter of City of Binghamton (Binghamton Firefighters, Local 729, AFL-CIO) (20 AD3d 859 [2005]) is misplaced. That case involved a reduction in staffing