N.M. Stat. § 77-9-41
It shall be unlawful for any person, firm or corporation to move, transport or cause to be transported from the state of New Mexico to any point beyond the limits thereof or within the state except as provided under Section 77-9-42 NMSA 1978, any horses, mules, asses, cattle, sheep or goats, or the carcasses thereof, by driving or in any motor or other vehicle or conveyance, unless such animal, animals or carcasses shall first have been inspected by an inspector of the New Mexico livestock board and unless, upon satisfactory showing of the ownership of said animals or carcasses, said inspector shall have issued inspection certificates in the form to be prescribed by the New Mexico livestock board and unless such certificate shall at all times accompany the animals or carcasses so being driven or transported in such motor or other vehicle; provided that no inspection shall be required where the transportation or movement from one point to another within the state is entirely upon lands exclusively within the control of the party moving or transporting or procuring the transporting of such animals or carcasses or is done under the provisions of Section 77-9-42 NMSA 1978 or when such transportation is authorized by the board to a location within the state.
NMS § 77-9-41