You can't e-file the state return without e-filing the federal in New Your to be best of my knowledge. You can try to e-file the state by itself to see if TurboTax will let you do that, otherwise you will have to mail in your state tax return.
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TurboTax is designed so that you must prepare a federal return before you can prepare a state return.
In order to file a state only return with TurboTax, you would start by preparing the federal return, then prepare the state return. You can’t e-file the federal return because you already filed, and you can’t e-file any state return unless you also e-file the federal return. (This is a security requirement.) So what you have to do is tell TurboTax that you will file both your state and federal returns by mail. Print the federal return and save it for your records. Print the state return, sign it, and mail it to the state tax authority at the address printed on the instruction page.
While it is true that New York State has a requirement that you must e-file if you use tax software, there is no penalty for filing on paper, and there is an exception in the law if the software has a situation where you can’t e-file. This would fall under that exception.
You could also print your New York State return, and then go to the New York State tax website, which I believe allows free online e-filing. You would copy the numbers from your printed turbo tax return onto the New York State e-file website and then file that way.
You can only efile state if Federal was efiled and accepted from the same account. So you will have to print and mail state.
Oh, do you need to prepare state? If you didn't use Turbo Tax for federal, There is a way but you first have to fill in the federal and pay for federal for it to flow to state. You will have to mail state. See,