N.M. Stat. § 61-23-28
When it becomes necessary by reason of the construction of public or private works to remove or obliterate any triangulation station, benchmark, corner, monument, stake, witness mark or other reference mark, it shall be the duty of the person in charge of the work to cause to be established by a licensed surveyor one or more permanent reference marks, which shall be plainly marked as witness corners or reference marks as near as practicable to the original mark and to record a map, field notes or both with the county clerk of the county wherein located, showing clearly the position of the marks established with reference to the position of the original mark. The surveys or measurements made to connect the reference marks with the original mark shall be of at least the same order of precision as the original survey.
NMS § 61-23-28