Each local or regional board of education of any town having a population of ten thousand or more shall, and each local or regional board of education of any town having a population of fewer than ten thousand may, appoint one or more legally qualified practitioners of medicine as school medical advisors. The advisor or advisors shall be assigned to the public school or schools within the limits of the school district. The boards shall provide such medical advisors with adequate facilities to conduct health examinations of individual pupils and to discharge such duties as may be prescribed by such board. In towns in which the board of health or department of health is maintaining such service substantially as required in connection with the school program of health supervision and other duties performed by school medical advisors, the board of health or department of health shall appoint and assign, with the consent of the local or regional board of education, such advisors. The board of education, with the approval of the director of health and with the consent of the chief executive officer of the town, may designate such town’s director of health, as provided under section 19a-200, or other town medical officers as the chief medical advisor for its public schools. Two or more boards of education may unite in the hiring and appointing of school medical advisors under arrangements for the payment of the expenses thereof and the performance of duties agreed upon by their boards of education. Each local or regional board of education shall prescribe the functions and duties of the school medical advisor in order that the program of health protection and health supervision, as outlined by such board and pursuant to the general statutes, shall be carried out.