State DOR Says I Owe, but TurboTax says I don't

First:  You need to print out your Indiana Schedule 5, and manually check the $$ amounts in each of the credit lines 1, 2, 3 that has $$ amount in them against what is on any of the forms, or other entries  you "think" entered into the software.  See if the totals match what should be there in the first place.    IF the $$ in any of lines 1,2,3 of the schedule 5 are wrong, and match what the Indiana DOR claims, then the problem was in the submission you made to IN.

But if submitted with the wrong numbers, it is likely (95%) and entry error on your part, not an actual software error.   IF there was a software error, the 5% of software error cases usually occur for in anyone filing early...i.e. before mid Feb.

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IF it is an error on the IN DOR's part, then you contact them at whatever way the letter indicates, and send them copies of all your forms that show Indiana withholding (or estimated tax payments, if appropriate) on them that supports the credit claims you had on on the Schedule 5.