N.M. Stat. § 62-10-9
Witnesses.
The commission and each of the commissioners, for the purposes mentioned in this
act, may administer oaths, examine witnesses at any hearing and certify official acts. In
case of failure on the part of any person or persons to comply with any lawful order of
the commission, or with any subpoena or subpoena duces tecum, or in the case of the
refusal of any witness to testify concerning any matter on which he may be interrogated
lawfully, any court of record of general jurisdiction or a judge thereof, may on application
of the commission or of a commissioner compel obedience by proceedings for contempt
as in the case of disobedience of the requirements of a subpoena issued from such a
court or a refusal to testify therein.