N.M. Stat. § 38-3-7
County to which case may be removed.
In all cases where a change of venue is granted, the case shall be removed to
another county within the same judicial district unless the remaining counties are
subject to exception, or unless the change of venue is ordered upon any of the grounds
relating to the judge. Under these circumstances, the case shall be removed to some
county of the nearest judicial district which is free from exception.