Local taxes from a different state

Indiana and Kentucky have reciprocal agreement.  This is an agreement between two states that allows residents of one state to request exemption from tax withholding in the other (reciprocal) state.

It seems you did not take advantage of that agreement.  In that case, because you worked in Kentucky, you paid the taxes in Kentucky.  I would contact the phone number on the Indiana tax notice and state:  "I paid my taxes in KY where I worked.  Can I amend my IN tax return and claim the out of state tax paid as a credit?"

The reciprocal agreement requires you to proactively sign the waiver.  If you did not do that you should be taxed in both the state you work in and your home state; however, you would get a credit in the home state or the taxes paid in the work state.