N.Y. ACG Law § 53

§ 53. County president form. A county which shall adopt the county\npresident form of government shall have a county executive to be called\n"county president." The office of county president shall be elective.\nThe term of office of the county president first elected shall be three\nyears from and including the first day of January of the second calendar\nyear in which the county president form becomes effective in the county.\nSuccessors shall be chosen by the electors of the county for terms of\nfour years each. A vacancy occurring otherwise than by expiration of\nterm shall be filled by appointment by the board of supervisors and the\nperson so appointed shall hold office until the commencement of the\ncalendar year next succeeding the first general election at which the\nvacancy may be filled. The county president may, when authorized by\nlocal law, serve as the head of one or more departments not administered\nby an elective official but without additional compensation. The board\nof supervisors of the county shall continue to have and exercise all the\nfunctions, powers and duties of boards of supervisors as now or\nhereafter provided by this chapter or by other law, except as limited or\notherwise provided by this section. The county president shall have\npower, as provided in subdivision five of section twenty of the\nmunicipal home rule law, to veto any local law passed by the board of\nsupervisors. The foregoing provisions of this section, together with\nother applicable provisions of this chapter, including those provisions\nof this chapter which may be made applicable, shall constitute the\ncounty president form of government authorized to be adopted by this\nchapter.\n