N.Y. SCC Law § 13

§ 13. Terms of office. The term of office of each elective officer,\nunless elected to fill a vacancy then existing, shall commence on the\nfirst day of January next succeeding his election. The term of office of\neach appointive officer shall commence on the day succeeding his\nappointment unless a different date is specified in the certificate of\nappointment. The term of office of the mayor, comptroller, treasurer and\npresident of the common council shall be two years. The term of office\nof alderman and supervisor shall be two years. The term of office of the\nassessors shall be four years, except that at the city election first\nheld in the city after the same shall have become a city of the second\nclass and the provisions of this chapter relating to the election of its\nofficers shall have become applicable thereto, two of the assessors\nshall be elected for a term of two years and two for a term of four\nyears. The term of office of the corporation counsel, city engineer,\ncommissioner of public works and sealer of weights and measures shall be\ntwo years, unless sooner removed by the mayor. The term of office of the\ncommissioner of public welfare shall be five years. Where the term of\noffice of an appointive officer is not specifically fixed by statute it\nshall be deemed to continue only during the pleasure of the officer,\nofficers, board or body authorized to make the appointment.\n