Yes, there's a way to enter the New York PTET Credit on a New York Nonresident Return (Form IT-203).
Per New York State Department of Taxation and Finance, taxes that are offset by a PTET credit are all taxes computed and reported on New York State personal income tax Forms IT-201, IT-203, and IT-205. If the PTET credit exceeds the tax due for the tax year, the excess credit will be refunded without interest.
Form IT-203 is the New York State Nonresident and Part-Year Resident Income Tax Return
NY has a page to show how the calculation is to be completed here.
The PTET Credit requires manual entry in TurboTax for Desktop using Forms Mode.
Open your return and click the Forms icon in the TurboTax header.
Click Open Form at the top of the left column.
Enter 653. Then click "IT-653: Pass-Through Entity Tax Credit" in the drop-down. Use "Copy 1" if asked to name the form. This will open the form in the large window.
Under Schedule A, enter the name (Col A), EIN (Col B), and PTET Credit Amount (Col C). If NYC tax was also paid, enter that amount in Col D.
You can verify your entry flows to IT-203 as a payment against any state taxes owed on your return.
When finished, click Step-by-Step in the header to return to the main screens.