The county comptroller within ten days after entering upon the duties of his office shall appoint a deputy comptroller. Such appointment shall be in writing under his hand and seal and be filed and recorded in the office of the county clerk. He shall perform such duties as may be assigned by the comptroller, and during the temporary absence of the comptroller he shall act as the comptroller and in the event of a vacancy in the office, he shall continue to act as such comptroller until a successor is elected or appointed and has qualified.
New York Legal Code