In all cases wherein the owner or operator of a motor vehicle which is on a public street has requested that the motor vehicle be left unattended at that location, in lieu of impoundment of the motor vehicle pursuant to § 14-502, the Police Department may honor said request for a period of time not exceeding 24 hours, after which time the motor vehicle shall either be removed from the location by the owner or operator or be impounded by the Police Department pursuant to § 14-504. The Police Department shall be immune from liability for any damage, loss or destruction of the motor vehicle occasioned by its being left unattended pursuant to the request of the owner or operator thereof, in lieu of impoundment. Nothing in this section shall be construed to limit the authority of the Police Department to order the removal of a motor vehicle by its owner or operator or to impound a motor vehicle pursuant to § 14-504 at any time whenever in his or her judgment the presence of the unattended motor vehicle constitutes a danger to the public safety.