The Mayor of the District of Columbia or his designated agent may refuse to register any motor vehicle or trailer which has not been inspected as required, or which is unsafe or improperly equipped, or otherwise unfit to be operated, and for like reason he may revoke or suspend any registration already made; provided, that the provisions of § 50-1403.01(a) shall be applicable in all cases where registration is refused, revoked, or suspended under the terms of this chapter.