N.Y. Town Law § 42
The town board of any town may at any time establish the office of deputy supervisor. The deputy supervisor shall be appointed by the supervisor to serve at the pleasure of the supervisor, and in case the office of supervisor becomes vacant any deputy supervisor in office at the time such vacancy occurs shall continue to serve until the successor of such deputy supervisor is appointed. If the supervisor shall fail to appoint a deputy supervisor within five days after the establishment of the office or within five days after a vacancy occurs in the office, the town board shall have power to appoint such deputy supervisor. During the absence or inability to act of the supervisor, or while the office of supervisor is vacant, the deputy supervisor shall preside, when present, at the meetings of the town board and shall be vested with all of the powers and may perform all of the duties of the supervisor under this chapter or any other law, except that he shall have no vote in his capacity as deputy supervisor on matters coming before the town board and he shall not serve as a member of the county board of supervisors. Any person, including a town officer, official or employee, may be appointed deputy supervisor, provided that the person appointed shall possess the same qualifications as an elective town officer. Before he shall perform any function as such, the deputy supervisor shall take and file the constitutional oath of office and execute and file an official undertaking in the manner prescribed in section twenty-five of this chapter. The town board shall fix the compensation which the deputy supervisor shall receive, which compensation may be in addition to any other compensation he may receive as a town officer, town official or town employee.
N.Y. Town Law § 42