Some states are fairly quick with refunds, while other states can take a long time processing returns--even several weeks--as they crack down on detecting fraudulent returns. Here are some things you should check:
First, you need to be sure your state return was successfully filed. If you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking at the Tax Home in your Online account. Does it show accepted, rejected, printed, started, ready to mail, or something else?
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
Only the state tax agency can know anything about your return.
FAQ: How do I track my Kentucky tax refund?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-kentucky-tax-refund/L9o...
Look at your actual state return to get the state refund amount. If your info is not showing up there, then phone Kentucky DOR and ask for the Individual Income Tax division to speak to a live agent there. Do NOT use their web email form with your personal info since that is not a safe and secure method to discuss sensitive information.