a. Subject to the provisions of subdivision b of this section, medical examination of a contributor in city-service accident disability and investigation of all statements and certifications by such contributor or on his or her behalf in connection therewith shall be made upon the application of the head of the agency in which the contributor is employed, or upon the application of a contributor or a person acting in his or her behalf:
(1) stating that such contributor is physically or mentally incapacitated for the performance of city-service, as a natural and proximate result of such city-service; and
(2) certifying the time, place and conditions of such city-service performed by such contributor resulting in such alleged disability and that such alleged disability was not the result of wilful negligence on the part of such contributor and that such contributor should, therefore, be retired.
b. The provisions of this section shall apply only where such application is based on an accident which occurred on or after July first, nineteen hundred seventy.
c. Any such application shall be filed within two years after the happening of such accident.
d. If such medical examination and investigation shows that any such contributor, by whom or with respect to whom an application is filed under this section, is physically or mentally incapacitated for the performance of city-service as a natural and proximate result of an accidental injury received in such city-service by reason of an accident which occurred on or after July first, nineteen hundred seventy and while a contributor, and that such disability was not the result of wilful negligence on the part of such contributor and that such contributor should be retired, the medical board shall so certify to the retirement board stating the time, place and conditions of such city-service performed by such contributor resulting in such disability, and the retirement board shall retire such contributor for accident disability forthwith.
e. If such application is denied solely on the ground that such contributor is not, at the time of such examination, physically or mentally incapacitated for the performance of city-service, such application may thereafter be renewed during such contributor's city-service at any time within five years from the happening of the accident but preceding the date on which such member shall have become eligible for service retirement, provided he or she submits himself or herself to such further examinations as the medical board may require.