You don't give us enough information to know whether or not there is an adverse party involved which may have insurance and caused the accident. If this was a single car accident and you do not have coverage for these damages, I suggest that you contact the impound yard immediately and work out an arrangement. Until the car is removed, you will, in all likelihood, be incurring storage fees.
Mr. Lundeen is licensed to practice law in Florida and Vermont. The response herein is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that, if known, could significantly change the reply and make it unsuitable. Mr. Lundeen strongly advises the questioner to confer with an attorney in your state in order to insure proper advice is received.
You are ultimately responsible for the storage fees regardless of who may be at fault. If the other party is at fault, then you can seek to recover the costs from the other party's insurer (if the other party is insured). But, in the meantime, you will need to pay for the fees and if you don't, then the tow company can auction off your vehicle. So, you cannot wait to get paid (if this option is possible) from the other party's insurance company and cannot argue with the tow or storage company that you should not have to pay the fees. This should not have an affect on your driving record.
Disclaimer: Please note that this is not meant to be legal advice and no attorney client relationship has been or is meant to be created with the above statements.
A roundup of the best tips and legal advice.