Why did my state return come in the mail. I had elected for direct deposit. Why did this happen? Worried my federal will do the same. How did their system mess this up?

You might have entered the wrong bank routing number or account number.

The feds and state have the right to send a paper check anytime they choose ... review your DD information for accuracy.

Here is how you can see your deposit information:

Your direct deposit information will be at the bottom of your Form 1040.

To view your 1040 after filing, Sign into TurboTax > Taxes > Tax Timeline > Some other things you can do > Download/print (.pdf). 

Please see the following FAQ article below if you entered in the wrong bank account information.

https://ttlc.intuit.com/questions/1901677

Once the IRS releases the refund (watch here https://www.irs.gov/Refunds ) it is then up to your bank to receive and post the deposit. This can take up to 3 business days to happen as they check to see if it is a legitimate deposit. If the routing & account numbers are correct AND if your name is on the account then the deposit should be acknowledged.  If any of these things are incorrect the bank can refuse the deposit and the IRS will convert the refund to a paper check mailed to the address on the return. This conversion process can take 2 weeks or more to happen.