Call a Personal Injury Attorney in your area and request a FREE fifteen minute consultaion. They can better advice you regarding the laws in your area.
As for a general concideration, the insurance companies will determine the degree of fault to be assigned to each driver for purposes of determining which coverage applies to the accident. If the other party had insurance, after they report an accident to their insurer, the company will investigate the circumstances of the accident and then make a liability decision of who's at fault based on the Fault Determination Rules.
If the other party has no insurance (which you better hope and pray that they don't), then their options include asking you to pay for the damage to their car, or pursuing a small claims action. If they do not proceed with pursuing the court proceedings, then you have nothing to worry about, technically.
However, with most insurance companies, you are at falt, their (the other party's to the accident) insurance company will send you a letter notifying you of the claim against you. They are going to offer you an amount to pay to settle the costs; medical, property damage, pain and suffering, etc.
If they do, accept it and don't try to take them to court. These insurance companies will usually work with you by designing a payment plan that fit your budget.
Make an agreement of the least amount that you can afford to pay. Make all of your payments on time. This will keep them off of your back, sorta say. Before you know it, you will have them all paid off and this whole situation behind your back.
I wouldn't really worry about it now, though. Hopefully, the other drive will have uninsured motorist in their full coverage insurance that will help to pay for their medical and hospital bills.
Hope this answers your question!
REFERENCE(S)
1. Law offices Doroshow, Pasquale, Krawitz and Bhaya, If
You Have Been Involved In An Accident(Online: Dplaw.com, 2006)
Law Offices of Doroshow, Pasquale, Krawitz & Bhaya | delaware lawyer | Attorney Delaware | Delaware Lawyers
2. aaron,
Car accident with no insurance(Online: ExpertLaw Forums, 2006)
Car accident with no insurance
3. Advocacy for Respect for Cyclists,
WHO'S AT FAULT(Online: ARC and Wikipedia Foundation, Inc., 1999)
Financial Services Commission of Ontario - Who's at fault?