N.M. Stat. § 4-33-10
Should an entire county having an outstanding indebtedness, bonded or otherwise, be taken so as to form a new county or be absorbed into another county already existing, it is hereby made the duty of the board of county commissioners of such new county, or of the county into which such entire new county may have been absorbed, annually to levy a tax which shall be assessed and collected by the assessor and collector of said county at the time and in the manner that other taxes are levied, assessed and collected in said county, unless such indebtedness has been otherwise provided for, upon all citizens, residents and property now subject or which may herein be subject to taxation within the limits of the county so taken or absorbed as herein mentioned sufficient to pay the interest or principal or both of such outstanding indebtedness in the same manner and to the same extent as was or would be required of the county commissioners of the county so taken or absorbed had the same not been taken or absorbed.
NMS § 4-33-10