Federal and state refunds are totally separate. The federal refund is sent by the federal government and the state refund is sent by the state government. If your state tax return shows a refund, you will get it from the state unless they adjust it for some reason. You can find the state web site to track it here: https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571
There is one federal government--your federal return goes to the IRS. If you get a federal refund it comes from the U.S. Treasury.
There are fifty states, of which thirty seven have a state income tax. If you get a tax refund from the state you live or work in, it will come from that state.
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.
Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 20 of your Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
On the IRS site you are also offered the use of an app called IRS2Go
https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved