No, there is no additional cost to e-file your state of NY return when using TurboTax Premier desktop version or the online version. However, all other states will have an e-file fee when using desktop software.
If you are in the CD/Download desktop 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.
