N.Y. Second Class Cities Law § 14
All elections of city officers, including supervisors and judicial officers of a city court or inferior local court, shall be held on the Tuesday succeeding the first Monday in November, and, except to fill vacancies, in an odd-numbered year. All such elections shall be held at the same time and places as the general election held in such year, and shall be conducted in all respects in the same manner as general elections in cities are required to be conducted, and all the provisions of law relative to such elections shall be applicable to the election for officers of the city. In case of the failure to elect an elective city officer, except as otherwise provided herein, the office shall be deemed to be vacant for the purpose of choosing a successor and the vacancy shall be filled in the manner provided herein for the filling of a vacancy in such office happening otherwise than by expiration of term.
N.Y. Second Class Cities Law § 14