N.M. Stat. § 73-2-59
Before proceeding to examine the land or lands over which the new ditch should be opened, the appraisers shall give the owner or owners of such land or lands, not less than three nor more than ten days' notice in writing of the time and place they will meet to examine and appraise said land or lands; such notice shall also contain a description as near as can be ascertained, of such proposed ditch, enlargement, extension or reconstruction, the point of entry and the direction thereof, upon said land or lands, and that at such time and place the said appraisers will hear and consider any evidence the owner or owners may desire to present as to the damages he or they will sustain by reason of his or their land or lands being so ditched. The notice herein provided for shall be served upon such owner or owners, and the returns made thereon by the constable of the precinct, or the sheriff of the county, in the same manner as service is made in civil cases, in justice of the peace courts [magistrate courts]; the notice and returns showing the manner in which the same was served shall be filed by the appraisers with the justice of the peace [magistrate] who appointed them, at the time they file their report.
NMS § 73-2-59