According to Texas Election Code § 172.003, "to receive a political party's nomination, a candidate in a primary election must receive a majority of the total number of votes received by all the candidates for the nomination." Following the March 3 primary elections, several House and Senate districts require a primary runoff before their candidates can be selected for the November election. Per Texas Election Code § 2.025, "a runoff election shall be held not earlier than the 20th or later than the 45th day after the date the final canvass of the main election is completed." The runoff date had been set for May 26, but the governor postponed it until July 14.
Special elections may be called per the law set out in Texas Election Code § 3.003. However, they can be postponed as needed in a disaster, as will be the case for the Senate District 14 special election. That election had been set for May 2, but the governor postponed it until July 14. The governor also issued a proclamation that allows political subdivisions to postpone their elections until November.