N.Y. ACG Law § 58

§ 58. Choice between election and appointment of officials. 1. The\noffice of comptroller, in a county where the office would otherwise be\nelective, or any elective county office that is being continued except\nthat of a supervisor or a judicial officer, may be made appointive by\nprovision therefor in the petition or resolution by which an alternative\nform of county government or a change in such a form is initiated and by\nvote of the people as provided in article fourteen. This option shall\napply to elective officers provided for in the constitution as well as\nto others. By like action the office of county commissioner of public\nwelfare, in a county where the office would otherwise be appointive, or\nany formerly elective office that has been made appointive pursuant to\nthis section, may be made elective. Whenever one of the options provided\nfor in this section is submitted to the people, it shall be submitted as\na separate question. Its adoption may, however, be made contingent on\nthe adoption of another question submitted at the same time if the\npetition or resolution by which it is initiated so provides.\n 2. Except as otherwise expressly provided in this chapter, every\nelective official of a county shall remain elective after the adoption\nof an alternative form of government and shall continue to perform the\nfunctions pertaining to his office.\n 3. When an office which could be made appointive remains or becomes\nelective under an alternative form of county government, the term of\nsuch office shall be four years from and including the first day of\nJanuary after each election to the office, except that the term of the\nfirst official elected to such office after the alternative form takes\neffect shall be three years if the term begins in an odd-numbered year.\nElections shall take place at the general elections in the last year of\neach term. When an appointive office is made elective, the first\nelection to the office shall take place at the next general election.\n 4. When an elective office is made appointive, the appointment shall\nbe made as provided in section two hundred two for a term coterminous\nwith the term of the county executive or board of supervisors making the\nappointment, except that it may be shortened as provided in subdivision\nthree if the office is made elective and that the person so appointed\nshall continue to serve until his successor is chosen and has qualified.\nIf a vacancy occurs in such an office, it shall be filled similarly by\nappointment for the balance of the term.\n