From the TurboTax FAQ:
New Jersey (NJ) automatically gives you a 6-month extension to October 15 if you filed a federal extension and have paid or withheld at least 80% of your total New Jersey tax liability. Otherwise, print and mail Form NJ-630 by April 15. If you owe taxes amounting to more than 20% of your total tax liability, submit payment by April 15 to avoid penalties. You can either include a check with Form NJ-630 or e-file your extension and pay online at their Individual Income Tax Payment and Filing site.