N.Y. Alt. County Gov't Law § 250
The head of the department of finance shall be the director of finance, except that in counties adopting the county administrator form, the head of the department shall be the county treasurer. The director of finance shall be appointed as provided in section two hundred two. In counties adopting the county manager form, the county director form or the county president form, the office of county treasurer is abolished and the functions, powers and duties of the office, except as otherwise expressly provided, shall devolve upon the department of finance. In a county in which the office of county treasurer is abolished, the county treasurer in office at the time the alternative form becomes effective in the county, shall perform the duties of director of finance, unless a vacancy otherwise occurs, until the expiration of the term for which he was elected county treasurer. Whenever in this chapter the term "director of finance" is used, it shall be deemed to mean and to refer to the county treasurer in counties adopting the county administrator form of government.
N.Y. Alt. County Gov't Law § 250