N.Y. County Law § 261
When a county district shall have been established, the board of supervisors shall appoint, designate or establish an officer, board or body as the administrative head or body of the district. All matters relating to the membership of such administrative head or body, including but not limited to, numbers, method of selection, tenure, qualifications and compensation, shall be determined by the board of supervisors. A member of the board of supervisors or any other county officer or official may be appointed as administrative head or as a member of the administrative body provided that he shall receive no additional salary or compensation for such services. The administrative head or body of one or more county districts shall be considered to be the administrative head or body of an administrative unit of county government. The title of such administrative head or body, if such functions are not conferred on an existing officer or body, and the name of such administrative unit, if the county district is made a separate administrative unit of county government, shall be prescribed by the board of supervisors, and such officer or body shall have all the powers generally conferred on heads of administrative units by this chapter, not inconsistent with the provisions of this article, and shall be subject to all of the duties imposed upon such heads by this chapter, not inconsistent with the provisions of this article.
N.Y. CountyLaw § 261