Is my taxes accepted by irs if it says accepted in Michigan and state taxes?

The IRS and Michigan tax agency are two different tax agencies, each doing their own thing.

It depends on how you are using the term "accepted" and whether you are confusing that term with "approved."

"Accepted" in TurboTax refers only to the efile status.  It means the IRS received your efiled return and agreed to start processing it.

After the IRS accepted the Federal return for processing, then the state would make a decision on whether to accept or reject the state efiled return.  If accepted, then the state begins processing the state return.

Once the returns go through processing, then each of those agencies will decide whether to approve it or not.  And the IRS and state tax agency will make that determination independently.

Here are some things you should check, some of which you may have already done:

If you efiled, double-check to be sure the returns were efiled successfully and accepted.
If you used Online TurboTax, you can sign into your Online Account and check the efile status at the Tax Home.

If that showed it was accepted, you can use the "Where's My Refund" tool at the IRS website below to monitor the status of your Federal refund.    Wait until at least 24 hours after acceptance before using the tool. 
https://www.irs.gov/Refunds

NOTE:

• When using that tool,  be sure to enter the correct SSN and filing status.  
• For the refund amount, use only the Federal refund amount, and not any total refund amount that includes a state refund.
• If you chose to pay TurboTax fees out of your Federal refund, then be sure to use the Federal refund amount before any fees were taken out.
• The amount to use is on your Federal Form 1040, Line 35a.
• You can also try phoning the IRS refund hotline.  I've seen it work for some users when the WMR tool didn't.  800-829-1954

FAQ:  How do I track my state refund?

https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571