Texas Election Code - ELEC § 212.022. Obtaining Initial Recount in Election on Office

(1) the difference in the number of votes received by the candidate and any candidate for the office who is shown by the election returns to be nominated, elected, or entitled to a place on a runoff ballot or tied for nomination, election, or entitlement to a place on a runoff ballot is less than 10 percent of that candidate's number of votes;

(2) the candidate is shown by the election returns to be entitled to a place on a runoff ballot or tied for nomination, election, or entitlement to a place on a runoff ballot;

(3) the secretary of state certifies that counting errors affecting the election occurred in one or more election precincts in which paper ballots were used, as provided by Section 212.034;  or

(4) the total number of votes received by all candidates for the office is less than 1,000 as shown by the election returns.