Can I request an extension of time to file if I cannot file my income tax return by the due date?

 Yes, you may obtain a six-month extension by filing online at our Online Income Tax Application for Automatic Six-Month Extension of Time to File. You can also file for a six-month extension by completing Form IT-370, Application for Automatic Six-Month Extension of Time to File for Individuals, or a six-month extension by filing Form IT-370-PF, Application for Automatic for Automatic Six-Month Extension of Time to File for Partnerships and Fiduciaries. In order to obtain an extension of time to file, full payment of the properly estimated tax balance must be made by the filing deadline. See What payment options are available if I owe tax with my extension?

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Income Tax - Filing due date
The NYS Department of Taxation and Finance Web site provides detailed information on when to file the State's income tax, including filing deadlines and extension information.
URL: http://www.tax.ny.gov/pit/file/income_tax_filing_due_dates.htm