Not sure what you mean, but a federal S corp needs to separately elect NJ S corp status.

In other words, you can be a federal S and NOT a NJ S. Since NJ S's have a minimum tax, using NJ S status means that the NJ taxable income passes to the owner's NJ 1040, potentially creating more income tax.

NJ S corp minimum plus NJ 1040 income tax on the passthrough income.