Texas Election Code - ELEC § 4.002. Authority Responsible for Giving Notice

(1) the county judge of each county wholly or partly in the territory covered by the election, for an election ordered by the governor;

(2) the presiding officer of the governing body of a political subdivision, for an election ordered by the presiding officer or the governing body;  and

(3) the authority ordering the election, for an election ordered by any other authority.