N.Y. Second Class Cities Law § 182

§ 182. Vacancy, how filled. When a vacancy shall occur, otherwise than\nby expiration of term, in the office of police justice, the same shall\nbe filled, for the balance of the unexpired term, at the next city\nelection happening not less than thirty days after such vacancy occurs.\nUntil such vacancy shall be so filled, the mayor may appoint a qualified\nattorney to fill the same, who shall hold office until the first day of\nJanuary after the election at which his successor is elected.\n