Medical examination of a member in city-service for accident disability and investigation of all statements and certifications by him or her or on his or her behalf in connection therewith shall be made upon the application of the commissioner, or upon the application of a member or of a person acting in his or her behalf, stating that such member is physically or mentally incapacitated for the performance of city-service, as a natural and proximate result of such city-service, and certifying the time, place and conditions of such city-service performed by such member resulting in such alleged disability and that such alleged disability was not the result of wilful negligence on the part of such member and that such member should, therefore, be retired. If such medical examination and investigation shows that such member 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 while a member, and that such disability was not the result of wilful negligence on the part of such member and that such member should be retired, the medical board shall so certify to the board, stating the time, place and conditions of such city-service performed by such member resulting in such disability, and such board shall retire such member for accident disability forthwith.