N.Y. County Law § 839
The county comptroller of the county of Oneida may, after entering upon the duties of his office, designate two of the assistants or clerks in his office deputy comptrollers. Such designation shall be in writing and shall be signed by the county comptroller and filed in the office of the county clerk. Such county comptroller shall also designate in writing and file in the office of the county clerk and the clerk of the board of supervisors the order in which such deputy comptrollers are to serve during his absence or inability to act. Before any such deputy so designated pursuant to the provisions of this section enters upon the performance of his duties, he shall take the constitutional oath of office. Either of such deputy comptrollers in the county of Oneida may perform such duties of the comptroller as may be assigned to him by an order of the comptroller to be entered in his office and shall also perform all the duties of the comptroller when the comptroller shall be absent from his office, or shall be incapable of performing the duties thereof, or when the office shall become vacant, until it shall be filled.
N.Y. CountyLaw § 839