Yes, punitive damages can be available in your accident case. It really depends on the situation. As far as obtaining punitive damages, you need special permission from the judge.
For example, it would have to proven to the judge that the negligence was not ordinary negligence; but that it was gross negligence to the point where there was some sort of danger to security, or to a person, created by the act of the other party that caused the accident.
So you would need that permission from the judge, first. If you did receive that permission, then you could pursue punitive damages.
It is important to speak to an attorney prior to taking any action in your case, such as this. So contact an attorney and explain the specifics of your case so that you can know what should be done in your case on this issue.