No you will not get a refund. Instead you will get a state tax credit on your NJ state income tax return.
Additionally, you may owe an amount on your NY state income tax return if you worked in NYC and your employer did not withhold NYC city taxes. (These NYC taxes can be high).
You will need to file as non-resident for NY (for your NY source income only - your NY wages). You will also need to file a NJ resident state tax return (for all income from all sources including NY wages). You will get a state tax credit in NJ for any NY state taxes that you paid on your nonresident NY state tax return.
You will want to work on your non-resident NY state tax return first. You will then take a tax credit from your non-resident NY taxes on your resident NJ state tax return. (Please note that you will only get a tax credit for your NY taxes up to the amount of NJ taxes that would have been paid if the income was earned in NJ).
Just follow the TurboTax guide when working on your states (remembering to do your non-resident 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
No you will not get a refund. Instead you will get a state tax credit on your NJ state income tax return.
Additionally, you may owe an amount on your NY state income tax return if you worked in NYC and your employer did not withhold NYC city taxes. (These NYC taxes can be high).
You will need to file as non-resident for NY (for your NY source income only - your NY wages). You will also need to file a NJ resident state tax return (for all income from all sources including NY wages). You will get a state tax credit in NJ for any NY state taxes that you paid on your nonresident NY state tax return.
You will want to work on your non-resident NY state tax return first. You will then take a tax credit from your non-resident NY taxes on your resident NJ state tax return. (Please note that you will only get a tax credit for your NY taxes up to the amount of NJ taxes that would have been paid if the income was earned in NJ).
Just follow the TurboTax guide when working on your states (remembering to do your non-resident 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