They should be liable under the facts you describe. The problem you have is that if they won't pay voluntarily, the only way to force the state to pay is by suing it--and in the meantime, you still owe the repair shop its money to get your car back. The state may owe you but it does not owe the repair shop, since they did not hire them to make the repairs. You have to pay the shop, then look to get your money back from the state. Also, there are special notice and paperwork requirments for suing the state, setting shorter deadlines and making it more complex than suing a private person or business: it is not easy for a nonlawyer to sue the state.