Election Code §43.004

(a) The governing body of each political subdivision authorized to hold elections, other than a county, shall designate the location of the polling place for each of its election precincts. (b) If a political subdivision holds an election on a uniform election date and is required to use the regular county election precincts, the political subdivision shall designate as the polling places for the election the regular county polling places in the county election precincts that contain territory from the political subdivision. (c) If a political subdivision holds an election jointly with an election described by Section 43.007 (a)(1), (2), (3), or (4) and is required to use countywide polling places under Section 43.007 , the governing body of the political subdivision may designate as the polling places for any required runoff election only the polling places located in the territory or in and near the territory of the political subdivision where eligible voters reside.