Upon making an application for the initial registration of a bicycle, the applicant shall be examined by an examining officer designated by the chief of police. The chief of police shall designate the scope and manner of the examination. Upon completion of such examination, the chief of police may refuse to issue a registration plate to the applicant if such examination discloses to the chief of police that the applicant does not have a reasonable knowledge of the provisions of this article or that the applicant is unable to exercise reasonable control in operating a bicycle.