If you are referring to direct deposit of your tax refund yes, you will need your routing number and account number.
Or if you are referring to paying your Turbotax fees: What forms of payment does TurboTax Online accept?
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Take me to my tax return
How you chose to receive the tax refund will be on the Filing Instructions page included with your tax return.
Sign onto your TurboTax online account - https://myturbotax.intuit.com/
Scroll down and click on Add a State. This will take you back to the 2019 online tax return.
Click on Tax Tools on the left side of the online program screen. Then click on Print Center. Then click on Print, save or preview this year's return.