Yes. If you are using TurboTax Deluxe CD/Download version, there is no e-filing fee for the state of New York or federal returns (they are included in purchase of the software). However, there is an e-file fee for all other states.
And if you are using TurboTax Deluxe Online there is also no e-file fee. Online products do not charge any e-filing fees.
If you are in the CD/Download version, go here https://turbotax.intuit.com/personal-taxes/cd-download/deluxe.jsp and click on Federal and state under the price. That opens a pop-up box that will have "E-file fees do not apply to New York state returns." at the very bottom.