To apply a portion of your state refund to next years taxes look for the section that deals with calculating estimated payments for 2016. Even if you don't need TurboTax to calculate the ES payments, the option to apply your refund will be within those screens. Each state return is set up a little differently in TurboTax and navigating directly to the section you need varies.
For New York, the section is toward the very end of your NY tax return. Past the 'Lets review your New York numbers' page. Look for the page called, "Additional Tax Situations" and start the section called Prepare Estimates or Apply Your Refund to 2017 (Form IT-2105) and click Start. Walk through these pages to apply your state refund to next years taxes. (screenshot attached)
