If an owner, manufacturer or dealer transfers his interest in a vehicle other than by the creation of a security interest, he shall, at the time of the delivery of the vehicle, execute an assignment and warranty of title to transferee in the space provided therefor on the certificate or as the Department of Motor Vehicles prescribes and cause the certificate and assignment to be mailed or delivered to the transferee or to the Department.

Except as provided in § 56-19-370, the transferee shall, promptly after delivery to him of the vehicle, execute the application for a new certificate of title in the space provided therefor on the certificate or as the Department prescribes and cause the certificate and application to be mailed or delivered to the Department.

Except as provided in § 56-19-370, and as between the parties, a transfer by an owner is not effective until the provisions of this section have been complied with.