N.M. Stat. § 42-2-16
Proof of payment; recording judgment.
After the petitioner has made payment in full to the clerk of the district court in
accordance with the judgment in the condemnation action, the clerk shall certify upon
the judgment that payment has been made thereon.
A copy of this judgment showing payment shall be recorded in the office of the
county clerk of the county in which the property is situate, and thereupon the title or
interest in the property affected shall vest in the petitioner.