Q. Just so I'm clear once I download the Ohio TT State software and enter the K-1 information it should adjust my Indiana income tax?
A. No. I'm not specifically familiar with the IN software (I have Ohio). But, the generic answer is: the home state software will ask if you paid state tax to another state on some of your IN income (which includes the K-1). It will allow you to enter the OH info (yes, it usually prepopulates some of the boxes).
That said, what are the sources of the Ohio income that you think you need to do an OH return.
