a. There shall be a medical board of three physicians constituted as follows:
1. One physician who shall be appointed by the members of the retirement board who are contributors.
2. One physician who shall be appointed by the members of the retirement board who are not contributors.
3. One physician who shall be appointed by the retirement board. Such physician shall be an expert in women's diseases or in diseases of the nervous system.
b. They shall be appointed to serve for a term of three years but the term of each shall expire on August first in different years. Vacancies shall be filled for the unexpired term. All appointments for a full term or for an unexpired term shall be made by the same group of members of the retirement board which appointed the predecessor.
c. All medical examinations required or authorized by sections 13-550 (relating to retirement of certain contributors for disability) and 13-551 (relating to retirement for accident disability) of the code shall be made by the medical board or by a physician or physicians designated by the medical board under rules and regulations for such designation prescribed by the retirement board, at the place of residence of the contributor or at a place designated by mutual agreement.