How do I pay the tax due for my state return once I have already e-filed the return?

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You must pay your state tax due using the state’s preferred method of receiving payment.  For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.

https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-pay...

https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue

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How do I review the method I chose to pay my federal/state  income tax with, after filing with TurboTax Online?

You can verify the tax payment method you chose on the Electronic Filing Instructions for your 2021 Federal Tax Return page, next to Balance Due/Refund. To see the page, follow these instructions:

1. Open your return if it’s not already open.
2. On the [Your name], your 2021federal return was accepted! screen, scroll down and select Add a State (don’t worry, we’re not adding a state) to access your tax forms and worksheets.
3. On the left side select Tax Tools then Print Center.
4. On the TurboTax Print Center screen, select Print, save or preview this year’s return.
5. On the next TurboTax Print Center screen, select 2021 federal returns and Include government and TurboTax worksheets (optional) then select View or print forms.
6. The information will be on the first page, Electronic Filing Instructions for your 2021 Federal or State Tax Return next to Balance Due/Refund.