N.Y. Second Class Cities Law § 71
There shall be a board of estimate and apportionment, which shall consist of the mayor, comptroller, corporation counsel, president of the common council, and the city engineer, except that when the number of subordinates, or the salaries thereof, in the department of any of the members of the said board are to be fixed and determined, the treasurer shall temporarily take the place of the member whose number of subordinates, or the salaries thereof, is under consideration, for the purpose of fixing such salaries or number of subordinates, and for that purpose alone. The members of the board shall meet upon the call of the mayor, or as directed by the board. The mayor shall be president of the board and the city clerk shall act as secretary thereof. The secretary shall keep a journal of all of the proceedings of the board.
N.Y. Second Class Cities Law § 71