Should paying additional tax for a 2016 dispute be entered on 2018 taxes?

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Did you pay additional federal tax or additional state tax?

If you paid additional federal tax, you do not enter it on your federal income tax return at all. A few states allow a deduction for federal tax that you paid. If you are in one of those states, you would have to check the rules for your state to see if you can include federal tax paid for an earlier year. The TurboTax state interview should make it clear. Read the screens carefully, and click any "Learn More" links.

If you paid additional state income tax, and you are itemizing deductions on your 2018 federal tax return, you can include any additional state tax that you paid in 2018. You deduct the state tax in the year that you pay it, no matter what year it is for. You can deduct only the actual tax, not any interest or penalties that you had to pay.