It is LIKELY you will need to file Form 1040, because your withheld NY and NJ state income taxes MAY exceed your $5,350 standard deduction.
If not, Form 1040EZ should be adequate.
As MukatA says, you must file a state tax returnfor BOTH NJ and NY.
When you file your NY return, you will need to file as a non-resident and pro-rate 20% of your salary as NY-sourced income. You will then be taxed on that 20% at NY state income tax rates.
Since 80% of your salary is NJ-sourced, I believe you will also pay NJ taxes (you pay on 100% of your salary), but you will get a credit for the NY taxes you paid that will reduce your NJ taxes somewhat. You will get a huge refund from NY, but then have to turn around and pay the bulk of that refund to NJ (since no NJ taxes were withheld). Expect to pay an under-withholding penalty to NJ.
If you need professional help to file your tax return, I have a number of clients in the NJ/NY area and can provide references. If you are interested, contact me at
[email protected].
TODAY, go to your employer and fill out the needed paperwork to have NJ taxes withheld from your paycheck. That way, when you file next year, you can avoid that under-withholding penalty.