N.M. Admin. Code § 17.11.28.16
Operators of correctional institutions have the authority to limit or deny access to institutional phones at times and in circumstances deemed proper by the correctional institution. However, no ICSP may take any action to discriminate among incarcerated persons in providing access to its tariffed telecommunications services at the correctional institutions. If telephone conversations carried on ICSP facilities are recorded, the ICSP shall provide a notice, via a recorded message, disclosing that fact to persons using the facilities. Pursuant to the correctional institution's procedures, the ICSP shall provide the means by which communications between incarcerated persons and their legal counsel, or counsel's staff, may be exempted from any requirement of the correctional institution that telephone conversations be recorded if permission is provided by the correctional institution. The incarcerated person, their counsel, or counsel's staff may request from the correctional institution that such calls be exempted from recording, and, if the correctional institution grants the request, the ICSP shall accommodate the request and provide verification of the exemption from recording.
N.M. Admin. Code § 17.11.28.16