Tex. Civil Practice and Remedies Code § 154.055

(a) A person appointed to facilitate an alternative dispute resolution procedure under this subchapter or under Chapter 152 relating to an alternative dispute resolution system established by counties, or appointed by the parties whether before or after the institution of formal judicial proceedings, who is a volunteer and who does not act with wanton and wilful disregard of the rights, safety, or property of another, is immune from civil liability for any act or omission within the course and scope of his or her duties or functions as an impartial third party. For purposes of this section, a volunteer impartial third party is a person who does not receive compensation in excess of reimbursement for expenses incurred or a stipend intended as reimbursement for expenses incurred.

(b) This section neither applies to nor is it intended to enlarge or diminish any rights or immunities enjoyed by an arbitrator participating in a binding arbitration pursuant to any applicable statute or treaty.