N.Y. ACG Law § 250

§ 250. Department of finance. The head of the department of finance\nshall be the director of finance, except that in counties adopting the\ncounty administrator form, the head of the department shall be the\ncounty treasurer. The director of finance shall be appointed as provided\nin section two hundred two. In counties adopting the county manager\nform, the county director form or the county president form, the office\nof county treasurer is abolished and the functions, powers and duties of\nthe office, except as otherwise expressly provided, shall devolve upon\nthe department of finance. In a county in which the office of county\ntreasurer is abolished, the county treasurer in office at the time the\nalternative form becomes effective in the county, shall perform the\nduties of director of finance, unless a vacancy otherwise occurs, until\nthe expiration of the term for which he was elected county treasurer.\nWhenever in this chapter the term "director of finance" is used, it\nshall be deemed to mean and to refer to the county treasurer in counties\nadopting the county administrator form of government.\n