N.M. Stat. § 48-6-5
When any rent or advances shall become due, or the tenant shall be about to remove from such leased or rented premises, or to remove his property from such premises, it shall be lawful for the person to whom the rent or advances are payable, his agent, attorney, assigns, heirs or legal representatives, to apply to a justice of the peace [magistrate] of the precinct where the premises are situated, or in which the property upon which a lien for rents or advances exist, may be found, or to any justice [magistrate] having jurisdiction of the cause of action, for a warrant to seize the property of such tenant; provided, that when a distress warrant shall be issued by any justice [magistrate], other than the justice of the peace [magistrate] of the precinct in which the rented premises may be situated, or in which the defendant may reside, such warrant shall be made returnable to, and the affidavit and bond upon which it is issued shall be transmitted by, the justice [magistrate] issuing such distress warrant, to the justice [magistrate] of the precinct in which the rented premises may be situated, or in which the defendant may reside.
NMS § 48-6-5