Legal Question in Civil Litigation in Texas

I'm not sure the city is correct. While the state is immune under the doctrine of "sovereign immunity", that immunity can be and often is waived. One statute that removes sovereign immunity for Texas governmental entities, including cities and municipalities is the Texas Tort Claims Act. This statute appears to address the removal of sovereign immunity for the events you describe.

I suggest you contact an attorney that handles traffic accidents. Be sure to have information on your out of pocket damages. If there is a police report, or any other written information that would be helpful as well.