State tax filing

TN doesn't have an income tax on wages.  You will owe state income tax to KY, since that's where you work. You have to file a KY Non-resident tax return.  Here's a link to the Kentucky tax instructions that may help explain things: <a rel="nofollow" target="_blank" href="http://revenue.ky.gov/NR/rdonlyres/42BA483C-F8C6-4EC2-B699-4CA88202BCBF/0/2015740NPPFINAL.pdf">http:...>

You should ask your employer to withhold KY state taxes if they aren't doing so already.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.