You should still file the NY state income tax return to avoid late filing penalties. You can file your NY state income tax return without paying the $4700.
- If you file an extension, you won't get a late filing penalty.
If you are going to file an extension, 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.
See
How do I file an IRS extension (Form 4868) in TurboTax Online? or
Do I need to file a state extension? If so, how do I do this?