N.Y. Second Class Cities Law § 14

§ 14. Elections. All elections of city officers, including supervisors\nand judicial officers of a city court or inferior local court, shall be\nheld on the Tuesday succeeding the first Monday in November, and, except\nto fill vacancies, in an odd-numbered year. All such elections shall be\nheld at the same time and places as the general election held in such\nyear, and shall be conducted in all respects in the same manner as\ngeneral elections in cities are required to be conducted, and all the\nprovisions of law relative to such elections shall be applicable to the\nelection for officers of the city. In case of the failure to elect an\nelective city officer, except as otherwise provided herein, the office\nshall be deemed to be vacant for the purpose of choosing a successor and\nthe vacancy shall be filled in the manner provided herein for the\nfilling of a vacancy in such office happening otherwise than by\nexpiration of term.\n