I used to be a NJ resident in 2015, but I lived and worked in PA for all of 2016. I received a W-2 for both NJ and PA for the same job. Do I have to file both?

Did you live in NJ for even a week? Did you inform your job of your move late? NJ taxes should have stopped once you moved.

I did notify them of my move late. I had been in PA since December and notified them of my address change in January.

The New Jersey taxes were withheld in error, so you need to get them back.

The easiest way to accomplish this is to input the W2 in the following manner (on the state portion, lines 15 to 17):

1. NJ Wages $0. List withholding as whatever it is. This will lead to you just getting it all back.
2. PA Wages: amount actually on the W2 plus the wages for the NJ portion. This will carry the correct wages to the PA return. The PA wages may be the same as federal wages.

You don't get a credit on your PA return for any taxes paid to NJ, but you will be getting them all back. If you corrected the mistake in January, this shouldn't have too large of an impact on your PA return, though it may cause you to owe a small amount while you wait for the NJ refund.

You don't need to use Turbo Tax to prepare this NJ return. You could just manually complete it, listing NJ source as $0 and attaching a statement describing your situation. But, you have to file with NJ if you want those taxes back- PA won't credit you for paying taxes to NJ.

http://www.state.nj.us/treasury/taxation/pdf/current/1040nr.pdf

Thank you so much for your response. I just want to make sure I understand it correctly. I will manually fill out and send the 1040NR for NJ, and then I will fill out my PA W2 on Turbo Tax. For your #1 you said "NJ wages $0 list withholding as whatever it is". Which line indicates what my withholding is? is that on my NJ w2 or PA one? And then for the second part of your response, does this mean I add line 16 (state wages, tips, etc.) from PA and line 16 from NJ and list that? And the same for line 17 (state income tax)?

When you type your W2 into Turbo Tax, lines 15 to 17... Put NJ wages as $0 and put your actual NJ tax withholding in Box 17. Your tax withholding for Box 17 is on Line 45 of the NJ return. If you decide to mail the NJ return and complete yourself, you put all 0s in the NJ column and your w2 box 17 (for NJ tax w/h only) on NJ return line 45.
You put your PA income inside Turbo as the total wages (probably the same as the federal wages). PA tax withheld is whatever you had withheld for PA.

Ok that helps so much. Do I do the same thing for boxes 18-20? Enter $0 for NJ local wages and the actual number for NJ local income tax?

There is no NJ local tax. If they put FLI  there, use the dropdown for box 14 and put it there.

And you don't get that tax back. SDI, FLI, SUI... you still pay them if you literally work in NJ. The reciprocal agreement doesn't cover those.

I have dollar amounts in box 18 (local wages, tips,etc.) and box 19 (local income tax) for my NJ one. I work in PA.

Nj doesn't have local income tax. Its the FLI tax... I live in NJ. I see the FLI there sometimes.

You don't zero out any PA local income since you are a PA resident. You only do that  to NJ state wages.