If you had no income to report on your tax return, then you would not need to file a return. If you did already file your Federal return by mail, then you would also have needed to file your state return by mail in order for it to have been considered 'filed'.
However, based on your statement about not having any income to report, neither return was likely to be required. If you were filing the return simply to qualify for the stimulus payment, but you would not normally file a return at all, then you can use one of the non-filer options to register for the stimulus payment.
Even if you already mailed your zero-income return to the IRS, it is not likely that it has been processed yet since they are not processing mailed returns at this time. Therefore, to trigger your stimulus payment, you can either use the TurboTax registration tool for non-filers (people not required to file a tax return) or register your information on the IRS site for non-filers. You can choose which one to use, but do not do both.
Here is the link for the TurboTax registration for non-filers. Scroll down the page and click the orange Register Now button: Register Now
Here is the link for the IRS registration for non-filers. Click the blue Non-Filers: Enter Payment Info Here button: Non-Filers Registration
Take a look at the following TurboTax article to help you decide if you need to file your return:
Do I need to file a Federal return this year?
@jenanna1709
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