N.Y. Educ. Law § 1914
For any central high school district formed on or after July first, nineteen hundred eighty-one, the order of the commissioner establishing such central high school district shall specify the number of members to constitute the board of education of such district and the number of members representing each of the districts included in such district. The number of members of such board shall be not less than five. There shall be at least one member of such board from each component school district. The board of education of each union free school district or central school district in such central high school district shall appoint the number of persons so designated by the commissioner to represent such district as members of the board of education thereof. In each common school district having a sole trustee, such trustee shall represent such district as a member of the board of education of such central high school district. If a common school district has three trustees, such board of trustees shall designate one of its members to represent such district as a member of such board of education. The persons so designated shall be members of the board of education of the central high school district during their terms of office as members of the board of education or as trustees of the districts respectively represented by them. Whenever a vacancy shall occur in the office of a member of the board of education of such central high school district, it shall be filled as above provided; except that each component school district may choose to fill vacancies from its district on the central high school district board by election.
N.Y. Educ. Law § 1914