N.M. Stat. § 35-6-6
Collection of fines, fees or costs.
A judgment and sentence issued by a magistrate court that includes an assessment
of fines, fees or costs shall constitute a money judgment that may be enforced in the
same manner as a civil judgment in the district court. The money judgment may be
assigned by the court to a public or private agency or business for collection purposes,
pursuant to the terms and conditions of a written agreement entered into by the court
and the agency or business.