Yes, you can sue a drunk driver in Kentucky even if it is a “no fault” state. “No fault” concerns the payment of medical expenses by your own insurance company. No fault doesn’t pertain to the actions of the other driver. Your personal injury lawyer will sue the at fault driver or resolve the case with their insurance company. Your own insurance company will then be entitled to repayment for the medical bills and lost wages they pay out through your “no fault” insurance. This money will come from the drunk driver and/or his/her insurance company.