Yes, the state withholding entered as part of your Federal return should automatically transfer to your state return.
Try deleting or removing your state return and starting it again. That will re-initiate the transfer process for all the data.
If you are using TurboTax Online, click the trash can icon or Delete next to your state. If you are using a CD/downloaded version of TurboTax, go to File > Remove State Return.
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