Constitution of the State of Texas 1876 Art. 3, § 13. Vacancy in legislature

(a) When vacancies occur in either House, the Governor, or the person exercising the power of the Governor, shall issue writs of election to fill such vacancies; and should the Governor fail to issue a writ of election to fill any such vacancy within twenty days after it occurs, the returning officer of the district in which such vacancy may have happened, shall be authorized to order an election for that purpose.

(b) The legislature may provide by general law for the filling of a vacancy in the legislature without an election if only one person qualifies and declares a candidacy in an election to fill the vacancy.