N.Y. Pub. Off. Law § 40

§ 40. Vacancy occurring in office of legislative appointee, during\nlegislative recess. When a vacancy shall occur or exist, otherwise than\nby expiration of term, during the recess of the legislature, in the\noffice of any officer appointed by the legislature, the governor shall\nappoint a person to fill the vacancy for a term which shall expire at\nthe end of twenty days from the commencement of the next meeting of the\nlegislature.\n