N.Y. Second Class Cities Law § 134

§ 134. Constitution of police and fire departments. The police and\nfire departments shall, as to their membership and component parts,\nremain as now constituted until the same shall be changed by action of\nthe common council. The common council has power at all times by\nordinance to determine the number of officers and members of each of\nsaid departments and the classes and grades into which they shall be\ndivided, except that it shall not have the power to diminish the number\nof the members of either of said departments as now fixed. The number of\nofficers or members of either of said departments shall not be increased\nwithout the approval of the board of estimate and apportionment. The\ncommon council may pass ordinances not inconsistent with law for the\ngovernment of the police and fire departments, and regulating the powers\nand duties of their officers and members. The commissioner shall\nappoint, as vacancies in said department occur, all officers and members\nthereof, and classify and apportion them into grades to conform to such\nordinances.\n