Please be aware that you are answering a question from Tax Year 2019.
First of all, there would not be a State Tax Balance Due Payment for the same tax year in which you received a State Refund, which is what this question is about.
State balance due is not computed because you are figuring if the prior year State Refund is taxable. (You pay a State Balance Due for Tax Year 2021 in Tax Year 2022 and so on) (In 2022 you would get a refund for Tax Year 2021 and so on) (so you never pay a State Balance Due the same year you get a State Refund.)
You are comparing what you claimed as Itemized Deduction on the prior year Federal Return, and that prior year STATE return resulted in a State Refund.
Your Federal return will use the state tax paid in that year as a possible deduction. Yes, you can include state tax balance due payments as well for the deduction.
But again, if you had a balance due, you didn't get a refund.
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