How do I know my amended state return was efiled

Did you actually amend, or just correct a rejected efile and resubmitted it?

I amended the return I sent yesterday because I forgot a credit to NYS.  This changed my status in New York from paying to a refund.  

Amended returns can not be e-filed. It has to be printed and mailed

There is a small set of state that are allowed to e-file Amended tax returns within TurboTax.

What state are you amending?

New York. It said it was sending it but do I receive a notification?

New York is one of the states allowing e-file of amended returns.
You can e-file one amended return within TurboTax. If you have to amend again, you'll need to print and mail.

Seeing if I can reach the correct person/group with the answer about getting the e-file status within the product. I would think that if you log back in, you should be able to see an e-file status. But, I'm trying to get a firmer answer.

I found someone that believes that you won't see e-file status within the product for the amended return. Have you checked email to see if you've received further emails about New York?