If the driver that caused the accident leaves the scene, you may still be able to file a personal injury claim. As soon as you can, you should immediately write down or commit to memory any information about the car that hit you and, if possible, a description of the driver who hit you and ran away. Connecticut law requires drivers to carry uninsured motorist insurance coverage for precisely these circumstances. This policy should cover the costs of all your injuries and pay for property damage in this situation, though you can run into the same obstacles you would with any other insurance company.