Tex. Const. art. IV, § 16

(a) There shall also be a Lieutenant Governor, who shall be chosen at every election for Governor by the same voters, in the same manner, continue in office for the same time, and possess the same qualifications. The voters shall distinguish for whom they vote as Governor and for whom as Lieutenant Governor.

(b) The Lieutenant Governor shall by virtue of his office be President of the Senate, and shall have, when in Committee of the Whole, a right to debate and vote on all questions; and when the Senate is equally divided to give the casting vote.

(c) In the case of the temporary inability or temporary disqualification of the Governor to serve, the impeachment of the Governor, or the absence of the Governor from the State, the Lieutenant Governor shall exercise the powers and authority appertaining to the office of Governor until the Governor becomes able or qualified to resume serving, is acquitted, or returns to the State.

(d) If the Governor refuses to serve or becomes permanently unable to serve, or if the office of Governor becomes vacant, the Lieutenant Governor becomes Governor for the remainder of the term being served by the Governor who refused or became unable to serve or vacated the office. On becoming Governor, the person vacates the office of Lieutenant Governor, and the resulting vacancy in the office of Lieutenant Governor shall be filled in the manner provided by Section 9, Article III, of this Constitution.