N.M. Stat. § 31-6-12
Subpoena powers; notice to witnesses.
A. The grand jury has power to order the attendance of witnesses before it, to cause
the production of all public and private records or other evidence relevant to its inquiry
and to enforce such power by subpoena issued on its own authority through the district
court convening the grand jury and executed by any public officer charged with the
execution of legal process of the district court; provided that all subpoenaed witnesses
shall be given a minimum of thirty-six hours' notice unless a shorter period is specifically
approved for each witness by a judge of the district court.
B. The target of the investigation shall not be subpoenaed except where it is found
by the prosecuting attorney to be essential to the investigation. If the target and his
attorney, if he has one, sign a document stating that the target will assert the fifth
amendment, he shall be excused from testifying on those matters as to which the
district judge determines he has a valid fifth-amendment privilege.
C. Subpoenas directed to witnesses shall be returnable only when the grand jury is
sitting.