N.M. Stat. § 33-3-21
Whenever in any incorporated town or village situated more than fifty miles from the county seat of the county in which such town or village is situated any person shall be tried before any magistrate whose precinct or any part thereof is embraced within such town or village for any offense against the laws of the state amounting to a misdemeanor and who shall be convicted thereof and be sentenced to be confined in the county jail, either as a part of the punishment inflicted for such offense or for the nonpayment of the fine and costs that may be assessed against the person, it shall be lawful for the sheriff receiving the order of commitment to confine the defendant in the jail belonging to such town or village for the period or term directed in the judgment or order of commitment. For the purposes of this [section] and Section 33-3-22 NMSA 1978, the jail of such town or village is hereby declared to be a county jail.
NMS § 33-3-21