This is just something that I've been wondering. If you think that your car has been wrongfully towed, do you need to pay the company and then sue them for your money back, or do they need to let you take your car back and then sue you for the money?
If you can persuade them to release the car without paying – but with a promise to pay – they could sue you to recover what you owe them for towing and storage (breech of contract). If not, you would have to sue them to recover the money you paid (which is the damage that they did to you). I cannot imagine a towing company releasing a vehicle without first being paid. There is no state which requires a towing company to release a towed vehicle just because the owner asks.
In general, it is the person who wants to change the status quo who initiates legal action.
If they still have your car and you want it back you need to petition the court for an order to release it. If you have your car and have paid them money you do not believe they were entitled to you need to sue to get it back. If you promised to pay them and they gave you your car a) they are idiots and b) they need to sue you for the money.