If I hit a car and the person leaves before the police show up am I still at fault?

If you were in an auto accident and the accident was your fault, your insurance is responsible for the repairs to the other party’s car. Your description leads me to believe that the person who you feel caused you to strike the other car is the one who left the scene, not the person you rear-ended. While you may feel the other person caused the accident, if there is no way to find out who that person was, then you are on the hook for the damages. You indicate you exchanged information, but it is not clear if you and that party collided. If not, then you would be responsible for the accident since that other person was not actually involved in the accident. If there was contact between you and the party who left, they could be charged with leaving the scene of the accident and if you have his information you should give it to the police to handle.