N.Y. PBO Law § 9

§ 9. Deputies, their appointment, number and duties. Every deputy,\nassistant, or other subordinate officer, whose appointment or election\nis not otherwise provided for, shall be appointed by his principal\nofficer, board or other body, and the number thereof, if not otherwise\nprescribed by law, shall be limited in the discretion of the appointing\npower. If there is but one deputy, he shall, unless otherwise prescribed\nby law, possess the powers and perform the duties of his principal\nduring the absence or inability to act of his principal, or during a\nvacancy in his principal's office. If there be two or more deputies of\nthe same officer, such officer may designate, in writing, the order in\nwhich the deputies shall act, in case of his absence from the office or\nhis inability to act, or in case of a vacancy in the office, and if he\nshall fail to make such designation, the deputy longest in office\npresent shall so act. If two or more deputies present shall have held\nthe office for the same period, the senior deputy in age shall so act.\nSuch written designation by a state officer shall be filed in the office\nof the secretary of state; and by any other officer, in the office of\nthe clerk of the county in which the principal has his office. If a\nvacancy in a public office shall be caused by the death of the\nincumbent, the deputies shall, unless otherwise provided by law,\ncontinue to hold office until the vacancy shall have been filled in\naccordance with law.\n