N.M. Stat. § 27-2-24
[Federal government entitled to share recovery.]
The federal government shall be entitled to a share of any amounts recovered under
the preceding two sections [27-2-22, 27-2-23 NMSA 1978] if required as a condition to
federal financial participation. The federal government's share shall be limited to a
percentage of the net recovery equal to the percentage of federal participation claimed
by the state for the payments when originally made. The amount due the United States
shall be paid promptly from the funds so collected to the United States government.