If you only need to amend your State return, go through the steps for a Federal amendment, and then prepare your State amendment.
The State return pulls info from your Federal return, so you need to go through the amended interview there, even if you don't need to amend your Federal return.
Then you will be able to print and mail your State Amendment only. You may want to wait until both your Federal and State returns have been accepted, and you have received your Refund, before preparing any Amended returns.
Click this link for more info on How to Amend a Return.
Here's more info on Amending Your Return you may find helpful.
I successfully amended my 2020 Federal return with TurboTax, but I lack confidence that TurboTax also filed the amended state return. How can I know the answer? TurboTax brought me down the road of checking and filing the amended state return but seemed to not finish the process. How can I know the status of the amended state return being complete and filed?
Do you live in Georgia, Michigan, New York, or Vermont? - only those states accept e-filed amended returns. Amended returns for all other states must be paper-filed.
If you live in one of those four states and are still concerned, there isn't any harm in printing and filing the amended state return by mail.
If amending in another state, you will have to print and file by mail.
In TurboTax, you can amend your State return without filing an amendment for your Federal.
I Need to Amend My State Return
Please see the information in this TurboTax FAQ here for assistance with amending your current state tax return.