N.M. Stat. § 59A-37-19
Any person may file with the superintendent a disclaimer of affiliation with any authorized insurer or a disclaimer may be filed by the authorized insurer or any member of an insurance holding company system. The disclaimer shall fully disclose all material relationships and bases for affiliation between the person and the insurer as well as the basis for disclaiming an affiliation. After a disclaimer has been filed, the insurer shall be relieved of any duty to register or report that may arise out of the insurer's relationship with the person unless and until the superintendent, within thirty days after the receipt of a complete disclaimer, disallows the disclaimer. The superintendent shall disallow such a disclaimer only after furnishing all parties in interest with notice and opportunity to be heard and after making specific findings of fact to support the disallowance.
NMS § 59A-37-19