Once a tax return has been Accepted by the IRS or a State, TurboTax receives no further information concerning the tax return or the status of any tax refund.
If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
Once your return is filed, TurboTax has no control over the processing of your return or the release of your refund.
Here are a couple FAQs to track your refund:
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?