Texas Government Code - GOV'T § 74.058. Duty to Serve When Assigned

(a) Except as provided by this chapter, a judge assigned by the presiding judge to a court in the same administrative region, or to a court in another administrative region at the request of the presiding judge of the other administrative region, shall serve in the court or administrative region to which he is assigned.

(b) The presiding judge of a judge's administrative region may relieve the judge of an assignment on presentation of good cause in writing by the assigned judge to the presiding judge.

(c) If the presiding judge refuses to relieve a judge from assignment after receiving from the judge a written statement declining the assignment for good cause, the judge may, not later than the fifth day after refusal by the presiding judge, petition the chief justice for relief from the assignment for good cause.  The chief justice may grant or refuse a petition for relief from assignment at his discretion.