How do i find the form to file a new york state extension when I owe taxes?

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See the following: NY Apply for an extension of time to file an income tax return

Although an extension gives you until October 15, 2019 to file your return, it won't give you extra time to pay your taxes, which are due on April 15, 2019 (June 15 if you're out of the country).

Even if you can't pay your taxes by the deadline, go ahead and file an extension anyway. Doing so will protect you from the late-filing penalty, which can be up to 10 times higher than the penalty for not paying your taxes on time.