So you never actually filed your state tax return. Sending a W-2 and a receipt is not filing a tax return. You have to file it now. That means completing Form N-11 and mailing it to the state.
Follow the instructions in the letter that you received for where to send your completed tax return. Send it by certified mail with a return receipt so you will have proof that they received it. Attach copies of your W-2 and the receipt for the child's car seat, even though you already sent them. Don't count on the Department of Taxation to match up things that were mailed separately. Keep a copy of everything you send.
Note that the deadline for claiming the credit for the car seat is December 31, 2021 (the end of this month, less than 4 weeks from now). So make sure you mail your properly completed and signed tax return in time to make sure that the Department of Taxation receives it by December 31.
You haven't said whether you are using TurboTax Online or the CD/Download TurboTax software. If you are using the CD/Download software, you can simply complete the state tax return in the software and print it for filing by mail. If you used TurboTax Online, you can no longer complete your 2020 state tax return online, because TurboTax Online has switched over to 2021. You have to use the CD/Download software to complete your tax return. The following FAQ has instructions for what you have to do.
How do I finish a prior-year return that I started in TurboTax Online?
(The first sentence of the FAQ says "2017, 2018, or 2019," but it now applies to 2020 also. The text of the FAQ just hasn't been updated.)
