You can only efile New York if your software allows it. And you can only efile state if you efile federal first. So if you didn't file federal or mailed it or already used the 5 efiles then Turbo Tax won't allow more efiles.
New York waived the penalty for not efiling back in April 2012. See this FAQ for more info,
https://ttlc.intuit.com/community/e-file/help/is-there-a-penalty-if-i-don-t-e-file-my-new-york-retur...
