N.M. Stat. § 42-2-7

A. Personal service, either within or without the state, of the petition, notice of condemnation and the notice of the preliminary order of entry, if any, shall be made and had in the manner as provided in the Rules of Civil Procedure, Rule 4(e), Subsections 1 to 6 inclusive, or as they may be amended.

B. If the name or residence of any owner be unknown, or if the owners or any of them do not reside within the state, or cannot be found therein, and are not served as hereinbefore provided, the required service and notice shall be given by publication of notice thereof for two consecutive weeks, the last publication to be at least three days prior to any default date, in a newspaper published in the county in which the proceedings are pending, if one is published in that county; if no newspaper is published in such county, then a newspaper published in another county, having a general circulation in the county wherein such proceedings are pending. When the address of any defendant who resides out of state is known to the petitioner, the publication shall be made as aforesaid and in addition, a copy of the petition and required notice thereof and the notice of the preliminary order entered, if any, shall be mailed to said defendant at such address, at least ten days prior to any default date on the preliminary order.

C. Personal service outside the state of any pleading or notice shall be equivalent to publication and mailing, and such personal service of the notice of entry of a preliminary order shall commence the running of the ten-day period within which objections may be made to the granting of a permanent order. Return of such service shall be by affidavit of the person making the same.