N.M. Stat. § 31-16-9
In order to facilitate representation in matters arising before appearance in any court in matters covered by the Indigent Defense Act, the director of the administrative office of the courts may, upon direction of the supreme court with respect to habeas corpus proceedings initiated in the supreme court, or upon request of a district court, enter into contracts with attorneys designated by these courts whereby the attorney shall undertake to perform the services of assigned counsel in all or any specified portion of the cases originating within the judicial district. All contracts shall be approved by the chief justice of the supreme court and all payments provided therein shall be made by the supreme court or in the appropriate district court requesting the contract, but in no instance shall contract payments exceed the maximums set out in Section 65 [31-16-8 NMSA 1978] of the Indigent Defense Act.
NMS § 31-16-9