N.M. Stat. § 27-14-14
Application of other law.
The application of a civil remedy pursuant to this law does not preclude the
application of other laws, statutes or regulatory remedy, except that a person may not
be liable for a civil remedy pursuant to the Medicaid False Claims Act and civil damages
or recovery pursuant to the Medicaid Fraud Act [30-44-1 NMSA 1978] if the civil remedy
and the civil damages or recoveries are assessed for the same conduct by another
government agency.