N.M. Admin. Code § 22.600.2.10
A hearing officer shall avoid impropriety. A hearing officer shall also avoid the reasonable appearance of impropriety. A reasonable appearance of impropriety occurs whenever a reasonable person would have serious doubts about whether the hearing officer could be fair given the circumstances. If the hearing officer, initially unaware of any potential issue, becomes aware of any potential appearance of impropriety during the course of the hearing, the hearing officer shall promptly disclose on the record the potential appearance of impropriety to the parties, allow the parties to appropriately respond or object, and then make a formal determination as to whether the hearing officer can continue to proceed in the hearing without violating this provision. The hearing officer may consult with other hearings officers and the chief hearing officer about any potential appearance of impropriety issues as part of the process of determining whether the assigned hearing officer can continuing presiding over the matter. The rule of necessity may require a hearing officer to proceed in the matter if there is no other hearing officer available to conduct the matter before expiration of a mandatory, jurisdictional deadline.
N.M. Admin. Code § 22.600.2.10