N.Y. Pub. Off. Law § 4

§ 4. Commencement of term of office. 1. The term of office of an\nelective officer, unless elected to fill a vacancy then existing, shall\ncommence on the first day of January next after his election, if the\ncommencement thereof be not otherwise fixed by law.\n 2. All terms of city officers, including supervisors, elected in any\ncity or part of a city, and of county officers in the city of New York,\nshall expire at the end of an odd-numbered year. Such officers shall be\nelected, except to fill a vacancy, at the general election in\nodd-numbered years. This subdivision shall not apply to any judicial\nofficer.\n