N.Y. Second Class Cities Law § 130
The commissioner of public safety shall be the head of the department of public safety. He may appoint, to hold office during his pleasure, a deputy, a health officer and a superintendent of buildings. Whenever a vacancy occurs in the office of the chief of police or chief of the fire department, the commissioner of public safety, shall appoint, in his discretion, a person deemed by him to be suitable and competent to fill the same. The chief of police and chief of the fire department shall each hold office during good behavior, or until permanently incapacitated or unfit to discharge his duties. The commissioner may appoint such other subordinates as may be prescribed by the board of estimate and apportionment to hold office, except as otherwise provided by law, during his pleasure. In case of the absence or disability of the commissioner or a vacancy in the office, the deputy shall discharge the duties of the office until the commissioner returns, his disability ceases or the vacancy is filled. Before entering upon the discharge of the duties of their respective offices, the commissioner, deputy, health officer, superintendent of buildings, chief of police and chief of the fire department shall each execute and file with the city clerk an official undertaking in such penal sum as may be prescribed by the common council.
N.Y. Second Class Cities Law § 130