N.Y. Second Class Cities Law § 133
The commissioner of public safety shall make, adopt and enforce such reasonable rules, orders and regulations, not inconsistent with law, as may be reasonably necessary to effect a prompt and efficient exercise of all the powers conferred and the performance of all duties imposed by law upon him or the department under his jurisdiction. He is authorized and empowered to make, adopt, promulgate and enforce reasonable rules, orders and regulations for the government, discipline, administration and disposition of the officers and members of the police and fire departments, and for the hearing, examination, investigation, trial and determination of charges made or prepared against any officer or member of said departments for neglect of official duty or incompetency or incapacity to perform his official duties or some delinquency seriously affecting his general character or fitness for the office, and may, in his discretion, punish any such officer or member found guilty thereof by reprimand, forfeiting and withholding pay for a specified time, supension during a fixed period or dismissal from office; but no officer or member of said departments shall be removed or otherwise punished for any other cause, nor until specific charges in writing have been preferred against and served upon him, and he shall have been found guilty thereof, after reasonable notice and upon due trial before said commissioner in the form and manner prescribed by law and the rules and regulations of the department.
N.Y. Second Class Cities Law § 133