Since your State return has been accepted, than TurboTax does not get any additional information about the processing of your return or the issuing of refunds. You can check your State's website for refund information.
How do I track my Pennsylvania tax refund?
Statement from the Department of Revenue: "If you filed electronically it takes approximately 4 weeks to process your tax return. However, if the department needs to verify information reported on your return or request additional information, the process will take longer. After your overpayment is processed, it normally takes an additional 3 to 4 weeks for your refund to be mailed or direct deposited."
You can track your refund on the Pennsylvania Department of Revenue's Where's My PA Personal Income Tax Refund? page.
The state will ask you to enter the exact amount of your expected refund in whole dollars. You can find this by signing in to TurboTax. If you're using the mobile app, you may need to scroll down to find your refund amount.
The refund date you'll see doesn't include the days your financial institution may take to process a direct deposit or the time a paper check may take to arrive in the mail. If you still have questions about your state tax refund, contact the Pennsylvania Department of Revenue.
As much as we would like to help, TurboTax does not distribute refunds, only the IRS or your state tax agency can legally do so.
