If you are engaged in some type of business, the cost of an accident that occurs during the course of business is usually a deductible business expense. Except that you can't deduct costs for doing something illegal. (For example, if you got a ticket for running a red light and were convicted and paid the fine, then you could not deduct damages you caused as a business expense.)
As noted, there is currently no federal deduction for personal casualty losses. You can list the loss in Turbotax because some states may allow a deduction if you itemize, but the thresholds for casualty losses are pretty high. The loss would have to be more than 10% of your income to even begin to be deductible on your state return.
