Post some info about the case, injuries sustained by the other party (to the best of your knowledge) and what your policy limits are. Then, someone may be able to give you a better idea.
Yes, if they sue, and a judgement is awarded higher than your policy limits, then you are responsible for the difference. However, depending on the circumstances, many personal injury cases settle before going to trial.
Give more details, and I'm sure more people will contribute to the thread.