I am a permanent resident of NJ but worked in VA temporarily and VA state taxes were deducted. The wages and state tax amount show on my W-2. Do I have to file in VA?

It depends but if you have to file a federal income tax return and you have VA sourced income (if you performed work in VA than you would have VA sourced income), you will need to file a VA nonresident state income tax return to report your VA income only.

You will also need to file an NJ resident state tax return (for all income from all sources including VA wages). You will get a state income tax credit in NJ for any VA state income taxes that you paid on your nonresident VA state income tax return.

You will want to work on your nonresident VA state income tax return first. You will then take a tax credit from your nonresident VA state income taxes on your resident NJ state income tax return. (Please note that you will only get a tax credit for your VA state income taxes up to the amount of NJ state income taxes that would have been paid if the income was earned in NJ).  The credit for taxes paid to another state section will be at the end of your residence state's interview process.

Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return.

Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)

https://ttlc.intuit.com/replies/3300797