We are an active duty military family and claim Kentucky as state of residence. Why is it saying I owe for state taxes?

You will not have to pay taxes to Kentucky on your military income since you are a resident of Kentucky. If you reported other income besides military income, then you may owe taxes.

It is possible that you did not indicate that you are military in the personal information section of TurboTax. Also, you may not have indicated that your W-2 income is from military when you entered it. Furthermore, there may have been a question about it in the Kentucky tax return section of TurboTax.

Also, if all of your income is from the military and you don't have any Kentucky tax withheld, you do not need to file a Kentucky tax return, so you could simply not file it if you can't get the issue resolved.