N.M. Admin. Code § 19.2.100.30
When two or more sealed highest and best bids received for the same tract of land are equal, the commissioner (if such highest and best bidders are present and cannot agree, by stipulation in writing, on how such tract shall be disposed of) shall call such equal highest and best bidders before the commissioner in the state land office (or if such sale is held in the county in which such lands are located, the person conducting such sale shall call such equal highest and best bidders before the person) on the same day such bids are opened, and again offer such tracts at auction to such bidders only, and grant such lease to the then highest and best bidder. If such bidders are not present when such bids are opened, then the commissioner will notify such bidders to submit sealed proposals within 10 days next following the date of the sale at which such bids were determined to be equal.
N.M. Admin. Code § 19.2.100.30