No. You are only required to file a resident Indiana return, since no Kentucky taxes were withheld. Indiana and Kentucky have a reciprocal agreement. This means that all salaries, wages, tips, and commissions earned in Kentucky by an Indiana resident must be reported as if they were earned in Indiana. If taxes have been withheld or paid to Kentucky, a nonresident return would have to be filed for a refund of state tax.
Since there were no Kentucky state tax withholding, you would not need to file a nonresident return for Kentucky. The way your husband's employer taxed him was correct.
If he has not already, your husband must submit Form 42A809 to his employer to make sure no Kentucky state tax is withheld in the future.
As far as the local taxes withheld, If you work in Kentucky and live in Indiana, you may get a credit or partial credit on your Indiana return for paying local tax to the Kentucky. This will depend on the rules and regulations of your resident county. If they do allow the credit, then you will see it on your interview screens when you are going through your Indiana state tax return.
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