N.Y. Second Class Cities Law § 15: Vacancies

§ 15. Vacancies. If a vacancy shall occur, otherwise than by

expiration of term, in an elective office of the city, including that of

supervisor, the mayor shall appoint a person to fill such vacancy. The

person so appointed to such vacancy shall hold office until the

commencement of the political year next succeeding the first annual

election after the happening of the vacancy at which a successor can be

elected for the balance of the unexpired term, if any. If a vacancy

shall occur in an appointive office of the city, otherwise than by

expiration of term, the officer, officers, board or body authorized to

make appointment to such office for the full term shall appoint a person

to fill such vacancy for the balance of the unexpired term.