N.M. Code R. § 20.11.82.24
A member of the board may participate in a meeting of the board by means of a conference telephone or other similar communications equipment when a medical or emergency situation exists that makes it extremely difficult or impossible for the member to attend the meeting in person, provided that each member participating by conference telephone or other device can be identified when speaking, all participants are able to hear each other at the same time, and members of the public attending the meeting are able to hear any member of the board who speaks at the meeting. A request to be present and vote by telephone or other similar device shall be made by the member to the chair or acting chair of the board. A board member who wishes to participate in a meeting in this manner must receive permission from the chair or acting chair of the board sufficiently in advance of the meeting so the hearing clerk can make adequate arrangements. The chair or acting chair shall determine whether a qualifying medical or emergency situation exists. The chair or acting chair who approves the request shall direct the hearing clerk to make arrangements. A board member's participation by such means shall constitute presence in person at the meeting. This provision shall not be used to allow a member to constitute a quorum of the board, and may only be used for the purposes of:
N.M. Code R. § 20.11.82.24