N.M. Stat. § 3-51-46
Passenger motor vehicles owned by and carrying a person with a disability and displaying special registration plates, or passenger motor vehicles carrying persons with severe mobility impairment and displaying parking placards, issued pursuant to Section 66-3-16 NMSA 1978, shall be permitted to park for unlimited periods of time in parking zones restricted as to length of time parking is normally permitted and are exempt from payment of any parking fee of the state or its political subdivisions, except that airport parking facilities may charge long-term parking fees for periods of time exceeding twenty-four hours. The provisions of this section shall prevail over any other law, rule or local ordinance but do not apply to zones where stopping, standing or parking is prohibited, zones reserved for special types of vehicles, zones where parking is prohibited during certain hours of the day in order to facilitate traffic during those hours when parking is prohibited and zones subject to similar regulation because parking presents a traffic hazard.
NMS § 3-51-46