Indiana and Kentucky have reciprocity, so your spouse's employer should have a form that shows this.https://revenue.ky.gov/Forms/42A809.pdf
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Q. Is his income considered out of state income?
When asked in the personal section if you earned income in another state, you should answer no. The fine print on that page tells you to do that due to the reciprocity agreement between IN & KY. If you answered yes, TurboTax is going to prompt you to do a return for KY. If you didn’t have any KY withholding you don’t need to do a KY return.
The reciprocity agreement does not apply to local city & county taxes. If you have KY local withholding in box 19 of your W-2, you can not get that refunded. Some (but not all) IN counties (but not the state) allow a credit, or partial credit for tax paid to another state city. That will come up in the IN state interview, if it applies in your case.