N.M. Stat. § 64-4-10
Whenever the owner or lessee of a registered aircraft transfers his title or interest thereto, the registration certificate and number issued for such aircraft shall remain with said aircraft. Upon a transfer or assignment of title or interest the owner or lessee shall endorse such assignment upon his certificate of registration, which statement shall be verified under oath by such owner or lessee. The owner or lessee shall deliver the certificate of registration and registration number to the purchaser or transferee at the time of delivery of the aircraft. If an aircraft is not registered at the time of purchase or lease, even though the aircraft may have been purchased within the state, new or used, the purchaser shall register it as provided herein.
NMS § 64-4-10