Texas Local Government Code - LOC GOV'T § 174.154. Arbitration Board

(a) Not later than the fifth day after the date an agreement to arbitrate is executed, each party shall:

(b) Not later than the 10th day after the date an agreement to arbitrate is executed, the arbitrators named under Subsection (a) shall attempt to select a third (neutral) arbitrator. If the arbitrators are unable to agree on a third arbitrator, either party may request the American Arbitration Association to select the third arbitrator, and the American Arbitration Association may appoint the third arbitrator according to its fair and regular procedures. Unless both parties consent, the third arbitrator may not be the same individual who served as a mediator under Section 174.151.

(c) The arbitrator selected under Subsection (b) presides over the arbitration board.