§ 160A‑388. Board of adjustment: "If an objection is raised to a member's participation and that member does not recuse himself or herself, the remaining members shall by majority vote rule on the objection."

§ 160A‑388.
"(e1) A member of the board or any other body exercising quasi‑judicial functions pursuant to this Article shall not participate in or vote on any quasi‑judicial matter in a manner that would violate affected persons' constitutional rights to an impartial decision maker. Impermissible conflicts include, but are not limited to, a member having a fixed opinion prior to hearing the matter that is not susceptible to change, undisclosed ex parte communications, a close familial, business, or other associational relationship with an affected person, or a financial interest in the outcome of the matter. If an objection is raised to a member's participation and that member does not recuse himself or herself, the remaining members shall by majority vote rule on the objection.

http://www.ncleg.net/EnactedLegislation/Statutes/HTML/BySection/Chapter_160A/GS_160A-388.html