Tex. Gov't Code § 507.024

The board shall adopt rules to provide for the safe transfer of defendants from counties to state jail felony facilities. A sheriff may transport defendants to a state jail felony facility if the sheriff is able to perform the service as economically as if the service were performed by the department. The department is responsible for the cost of transportation of defendants to a state jail felony facility. Defendants may be transported with other persons being transported to the custody of the department provided appropriate security precautions prescribed by policies of the department are taken.