I got an email from TT saying federal and state tax return was rejected however the tax software indicates that the return has been accepted. How do I handle this?

After you e-file your return, it's considered "pending". After the IRS processes your return, it'll either be accepted or rejected.

 

Once you submit your return in TurboTax Online, you'll see its status on the Tax Home screen of your account. We'll also send you emails letting you know when your e-file status changes.

 

You can use the IRS tool Where's My Refund to check if your e-filed return has been received.

 

If you don't see an e-file status for your return in TurboTax Online, you may have filed your return in a different account or using a different method.

If you used TurboTax Desktop:

1. Select File.
2. Select Check E-file status.

 

If your return is rejected, you should have received guidance on how to fix the rejection so that you could e-file.

TT says federal return accepted and state is pending, but I received email from intuit saying that return was rejected. 
I went to the Desktop app and did status check and it still says federal returns accepted. So which is correct?

You can check that your return was received by the taxing authority  using these instructions: Check the Electronic Postmark of your Return. Pay close attention to the separate lines for Federal and State. They are separate statuses.