Hi Everyone,
I am a bit confused and would appreciate your help.
My wife arrived in the US on July 8th on H4. I just completed filing a joing federal tax (on the computer, I will print, and attach the W7 and notarized passport copy)

But am confused on how to handle NJ state tax. Should I file a joint here as well? And what should I do about the social security number?

Thanks for your help

Yes, you can file jointly for NJ, but you must wait until the IRS sends her the ITIN back, which will happen about a month after you mail it in.