Yes, unfortunately with only liability coverage on your vehicle you will have to pay to get your windshield replaced in Kentucky.
If you had Kentucky-based comprehensive insurance, KY state law states that your insurance company will waive the deductible for windshield repair or replacement, which means no out-of-pocket expense for you.
Since if you have comprehensive insurance coverage in the state of Kentucky, the deductible is waived you would not have to pay for the repair or replacement of your windshield but with only liability you vehicle is not covered for glass damage in order to have the deductible waived.
To get a quote for KY comprehensive auto insurance follow this link.