Texas Election Code - ELEC § 2.028. Tie Vote in Runoff

(a) Except as provided by Subsection (c), if the candidates in a runoff election tie, an automatic recount shall be conducted in accordance with Chapter 216.  If the recount does not resolve the tie, the tied candidates shall cast lots to determine the winner.

(b) The presiding officer of the final canvassing authority shall supervise the casting of lots under this section.

(c) A tying candidate may resolve the tie by filing with the presiding officer of the final canvassing authority a written statement of withdrawal signed and sworn to by the candidate.  If the statement of withdrawal is received before the automatic recount is conducted, the remaining candidate is the winner, and the automatic recount is not conducted.  If the statement of withdrawal is received not later than 5 p.m. the day after the date the automatic recount is conducted, the remaining candidate is the winner, and a casting of lots is not held.