Section 344 - County or part-county boards of health; terms of office; vacancies1. The term of office of each appointive member of the board of health of a county or part-county health district, including the additional city representative members shall be six years, and the term of one of the members shall expire annually; except that the term of office of the representative member of the board of supervisors shall be for such lesser period as may be required in the event that he does not continue as a member of the board of supervisors.2. Upon the establishment of a new county or part-county health district, the first appointments shall be made for the respective terms of six, five, four, three, two and one years.3. Vacancies shall be filled by appointment for the unexpired terms.N.Y. Pub. Health Law § 344