(a) Except as provided in § 31-3.1-2, every owner of a vehicle which is in this state and for which no certificate of title has been issued by the division of motor vehicles shall make application to the division for a certificate of title of the vehicle.
(b) The division of motor vehicles shall not register or renew the registration of a vehicle unless a certificate of title has been issued by the division to the owner or an application for title has been delivered by the owner to the division.