N.M. Stat. § 4-33-8
Whenever a part of the territory embraced within the limits of any county of this state having outstanding indebtedness, bonded or otherwise, is taken to form a new county or to add to the area of a county already in existence, nothing in this article [4-33-8 and 4-33-9 NMSA 1978] shall be construed to release any of the citizens or property, subject at that time or which may thereafter become subject to taxation within the exterior boundaries of the territory so taken, unless such indebtedness has been otherwise provided for, and the board of county commissioners of such new county or of the county to which such territory has been added is hereby authorized and required to levy annually a tax which shall be assessed and collected by the assessor and collector at the time and in the manner that other taxes are assessed, levied and collected in said county upon all the citizens and residents and property subject or which may thereafter become subject to taxation within the limits of the territory so taken as the same legally existed and is established at the time the said territory is taken: provided, that said tax shall be uniform between the county gaining and the county losing the territory. The board of county commissioners of the county whose territory has been taken shall notify the board of county commissioners of such new county to which territory has been added of the amount of the levy and for the purposes above specified immediately upon the same being made; and no adjournment of either board of county commissioners, when convened for making the levies for the purposes of taxation, shall be had until the levy herein provided for in this article shall have been made.
NMS § 4-33-8