N.M. Stat. § 73-16-19
County takes property subject to lien of district
assessments.
When any county shall take and hold any tax sale certificate or the title to any
property under the provisions of this act, or of any taxing act of this state, such taking
and holding shall be subject to the lien and charge of all district assessments, made,
levied and assessed under the provisions of this act, and such district assessments
shall be and become collectible as are other district assessments when the tax sale
certificate or title to property taken and held by the county shall by sale or assignment
become vested in any person.