New York Public Officers Law
Commencement of Term of Office
1. The term of office of an elective officer, unless elected to fill a vacancy then existing, shall commence on the first day of January next after his election, if the commencement thereof be not otherwise fixed by law.
2. All terms of city officers, including supervisors, elected in any city or part of a city, and of county officers in the city of New York, shall expire at the end of an odd-numbered year. Such officers shall be elected, except to fill a vacancy, at the general election in odd-numbered years. This subdivision shall not apply to any judicial officer.