N.M. Stat. § 73-2-57
Should they deem it necessary, the mayordomo may cut through the lands of any person or persons, by first obtaining their consent, by the community of such ditch offering to pay a compensation, to be agreed upon between the owner or owners of the lands through which the ditch is to be opened, and the parties interested in the said ditch. If the owner or owners, who shall be solicited to permit their lands to be ditched, in the cases mentioned in the preceding section [73-2-56 NMSA 1978], should improperly refues [refuse] or decline to accept the compensation offered by the parties interested in such ditch, or ask a compensation which the parties interested do not agree to on account of its exorbitance, in such case the mayordomo of said ditch shall lay the case before the justice of the peace [magistrate court] of the precinct in which such ditch may be situated, and it shall be the duty of the justice of the peace [magistrate court], to whom the case is presented, to appoint three men, experts, of known integrity, to establish a just compensation to be paid to the owner or owners solicited to permit their lands to be ditched through in the cases above mentioned.
NMS § 73-2-57