N.Y. Second Class Cities Law § 142
The members of the police department, other than surgeons, in criminal matters have all the powers of police officers under the general laws of the state, and they shall also have the power and it shall be their duty to arrest any person found by them violating any of the penal ordinances of the city or laws of the state, and to take such person before the proper city magistrate. Such person shall be dealt with in the same manner as if he had been arrested upon a warrant theretofore duly issued by such magistrate. They shall report violations of law and ordinances coming to their knowledge in any way under regulations to be prescribed by the commissioner of public safety. They shall also have, in every other part of the state, in criminal matters all the powers of constables and any warrant for search or arrest issued by any magistrate of the state may be executed by them in any part of the state according to the tenor thereof without indorsement. They shall possess such other powers and perform such other duties as may be provided by law or ordinance of the common council.
N.Y. Second Class Cities Law § 142