When any firefighter desires to become a member of the relief association provided by this chapter, that firefighter may apply in writing for membership to the association. The application must be made on a form supplied by the association and must be accompanied by the certificate of a physician as required by the association’s bylaws. The application and certificate must be filed with the secretary of the association, with required fees, and thereafter the board of examiners of the association shall make an investigation and file its report concerning the application with the secretary.