Texas Election Code - ELEC § 51.003. Procuring and Allocating Supplies

(1) for an election ordered by the governor or a county authority, the county clerk, subject to the approval of the county election board;

(2) for a primary election, the county chair of the political party holding the primary, subject to the approval of the party's county executive committee;

(3) for an election ordered by a city authority, the city secretary;  and

(4) for an election ordered by an authority of a political subdivision other than a county or city, the secretary of the subdivision's governing body or, if the governing body has no secretary, the governing body's presiding officer.