A past year return cannot be e-filed. The only way to file it is by mail. So you will need to print it, sign and date it in ink, and mail it to the state.
You have not mentioned whether you have already prepared the state return, or whether you used TurboTax to prepare your federal return. We need to know those things in order to be helpful and tell you what to do next.
Go to your state tax website for the prior year 2022 state tax forms and schedules which you can download, complete and mail back to your state.
If you used TurboTax online editions for tax year 2022 you would need to purchase and download one of the 2022 desktop editions to install on a personal computer. Download the 2022 tax data file. Open the 2022 tax return with the installed 2022 TurboTax desktop program and download a state program. Complete the state return. Print and mail the state return to your state.
To complete and file a 2022 tax return using TurboTax you would need to purchase, download and install on a personal computer one of the 2022 desktop editions from this website - https://turbotax.intuit.com/personal-taxes/past-years-products/
A 2022 tax return can only be printed and mailed, it cannot be e-filed using TurboTax.
To access your prior year online tax returns sign onto the TurboTax website with the User ID you used to create the account - https://myturbotax.intuit.com/
Start the 2023 online tax return by entering some personal information then click on Tax Home on the left side of the screen.
On the Tax Home webpage -
Scroll down to the section Your tax returns & documents. Click on the Year 2022 and Click on Download .tax file