N.M. Stat. § 73-10-38
The secretary of the board of directors shall cause a notice of the filing of such petition to be published for at least three weeks in some newspaper published in the county where the office of the board of directors is situated, and if any portion of said district lie within another county or counties, then said notice shall be so published in a newspaper published within each of said counties; or if no newspaper be published therein, then by posting such notice for the same time in at least three public places in said district, and in case of the posting of said notices, one of the said notices must be so posted on the lands proposed to be excluded. The notice shall state the filing of such petition, the names of the petitioners, description of the lands mentioned in said petition and the prayer of said petitioners; and it shall notify all persons interested to appear at the office of said board at a time named in said notice, and show cause in writing, if any they have, why said petition should not be granted. The time to be specified in the notice at which they shall be required to show cause shall be the regular meeting of the board next after the expiration of the time for the publication of the notice. The petitioner or petitioners shall advance to the secretary sufficient money to pay the estimated cost of all proceedings under the petition before the secretary shall give such notice.
NMS § 73-10-38