Redistricting authority:  
U.S. Congressional Districts – Legislative. See below.

State Legislative Districts – Legislative/Board. “The Texas Legislature has primary responsibility for redistricting state Senate, state House, and U.S. Congressional seats. The Texas Constitution requires the Legislature to redistrict House and Senate seats during its first regular session following publication of each United States decennial census. The Legislative Redistricting Board, composed of the Lieutenant Governor, Speaker of the House, Attorney General, Comptroller, and Land Commissioner, was created by constitutional amendment in 1951, at least in part to provide legislators with an incentive to redistrict after each federal decennial census. If the Legislature fails to redistrict House or Senate districts during the first regular session following release of the decennial census, Section 28, Article III, of the Texas Constitution requires the board to meet within 90 days of the end of that regular session and, within 60 days of convening, to adopt its own House or Senate plan to fill the void left by the Legislature’s failure. The Legislative Redistricting Board’s duty to redistrict is also invoked if a House or Senate plan passed by the Legislature at that regular session is vetoed or held invalid in court.  The Governor has veto power over the Legislature’s plans, but not over the board’s plans. (http://www.tlc.state.tx.us/redist/process_lrb.htm)