After you file

If your NYS Tax return is under review you should have received a letter explaining why it is under review and a request to provide additional documentation if necessary.  In many cases they are requesting verification of income / taxes paid so they are requesting copies of W-2's; 1099s etc.  

Under NYS law once you replied to this letter and furnished the required information the Tax Dept has 90 days to review before you can inquire as to why payment is delayed.