Who is liable if you are a cosigner and the primary driver has an accident and is charged with DUI?

As long as the driver has auto insurance on the vehicle there should be no problem, DUI or not. If there is no insurance on the vehicle you have a problem. In that case not only will you be liable for the damage to the vehicle you cosigned but you also may have liability for the injuries and damages for anyone they hit. You should be very careful about cosigning a loan with anyone. They will get payment from the one who is easiest to get payment from and that is you most likely.