N.M. Stat. § 59A-32-20
Any rental car company offering for sale insurance coverage or collision damage waivers shall state clearly on the front page of the rental contract that the purchaser of the insurance coverage or collision damage waiver offered may be covered for such claims on his personal motor vehicle insurance policy and that if such insurance coverage exists under the renter's personal insurance policy, and the coverage is confirmed, the renter may require that the rental car company must submit any claims to the renter's personal insurance carrier as the renter's agent. The rental car company shall not make any written or oral representations that it will not present claims or negotiate with the renter's insurance carrier. For purposes of this section, confirmation of coverage includes telephone confirmation from an insurance company representative.
NMS § 59A-32-20