Unfortunately, Turbotax can't e-file a state return unless the federal return was also e-filed. This is a security measure to prevent scammers from filing multiple state returns, and I believe it applies to all consumer-level tax software.
A professional might be able to e-file a state return, but you would have to pay for that separately.
Some states allow e-filing directly on their web site, but New York is not one, they just point you to consumer software.
You will have to print, sign and mail your return.
