N.M. Stat. § 67-4-13
All county roads and bridges shall be maintained at the expense of the respective counties. All roads, and bridges upon roads, that have been declared to be a state highway by acts of the legislature or resolution of the state transportation commission shall be maintained at the expense of the state, provided, that whenever there are not sufficient funds available in the state road fund for maintenance of all state highway mileage in any county, the state transportation commission shall certify to the board of county commissioners of the county the sections of highways that it is unable to maintain at state expense, and these sections shall thereafter be maintained at the expense of the county until such time as there are state funds available to maintain them.
NMS § 67-4-13