Tex. Labor Code § 406.034

(a) Except as otherwise provided by law, unless the employee gives notice as provided by Subsection (b), an employee of an employer waives the employee's right of action at common law or under a statute of this state to recover damages for personal injuries or death sustained in the course and scope of the employment.

(b) An employee who desires to retain the common-law right of action to recover damages for personal injuries or death shall notify the employer in writing that the employee waives coverage under this subtitle and retains all rights of action under common law. The employee must notify the employer not later than the fifth day after the date on which the employee:

(1) begins the employment; or

(2) receives written notice from the employer that the employer has obtained workers' compensation insurance coverage if the employer is not a covered employer at the time of the employment but later obtains the coverage.

(c) An employer may not require an employee to retain common-law rights under this section as a condition of employment.

(d) An employee who elects to retain the right of action or a legal beneficiary of that employee may bring a cause of action for damages for injuries sustained in the course and scope of the employment under common law or under a statute of this state. Notwithstanding Section 406.033, the cause of action is subject to all defenses available under common law and the statutes of this state unless the employee has waived coverage in connection with an agreement with the employer.