Meetings subject to the attorney-client privilege pertaining to threatened or pending litigation in which the public body is or may become a participant may be closed. However, there must be a credible threat of a lawsuit. NMSA 1978 § 10-15-1-H (7)

As a general rule, the public body’s attorney should be present in the closed meeting, either in person or by telephone. Note that there is no general attorney-client privilege exception to close a meeting unless the public body is involved in threatened or actual litigation. AG OMA Guide Commentary, p.29