No, the IRS would not have your direct deposit information that was entered with your state return.  If you direct deposited a Federal refund from 2018, then they would use that information.  

The best thing for you to do is to wait a few more days until the IRS activates a tool on their site that will allow you to enter your direct deposit information and check the status of your stimulus payment.  It is called Get My Payment.  You can find it through the IRS link shown below.

Use the following links to keep up with the latest developments:

IRS -- Economic Impact Payments

TurboTax Corona Virus Tax Center

@scbarr5160

How would I specify State Refund Direct Deposit info if I am not getting a refund from the Federal return? TT does not seem to allow me to enter this account information when filing my state return via the mail instead of paying the $19.95 fee. This is very frustrating.

No, your state information will not be registered with the IRS.  There is an option on the IRS Get My Payment website to enter your deposit information.  If the IRS has no bank information on file for you, they will mail you a paper check or a debit card.

Thanks Mary, I was looking for a way to get my bank information into my state return to receive a direct deposit of an overpayment. TT only seems to allow input of banking info I would have had a federal refund due to me, which is not my particular case. Thanks for your response!