No, taxes paid to your state are not then tax deductions for the state.
However, if you are able to itemize on your federal return you can claim the prior year state taxes paid on your federal return.
In the "Deductions & Credits" tab,
- Scroll down to "Estimates and Other Taxes Paid"
- "Show More"
- "Start/revisit" the "Income Taxes Paid" topic
- Scroll down to "Other Income Taxes paid in 2020"
- "Start/revisit" "Taxes paid for 2018 or prior year..."
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