It depends on your state of residence.
No - If you are a NJ or PA permanent resident and you are working at a NJ office/branch located in NJ but the company's headquarters is in NY.
In this instance, you will only need to file a NJ resident state income tax return.
Yes - If you are a NJ permanent resident and you are working remotely in NJ for a NY based company.
When it comes to filing state taxes, you will report income in the state were the work is performed However, NY is one of the few states that will also require you to file in NY if you work remotely but the company is based in NY.
You will also need to report your wages in the state where you are a permanent resident (if that state has a personal state income tax filing requirement).
So if you worked in NY or if you worked remotely for a company is located in NY but you are a resident of another state, you will need to file a NY nonresident state income tax return to report your NY-source income. (If NJ is not your state of residence and you worked in NJ , then you will file a NJ nonresident state income tax return to report NJ-source income and an resident state income tax return. This does not apply to PA residents under the wage reciprocal agreement.)
You will then be able to get a tax credit on your resident state income tax return for taxes paid on your nonresident state income tax return. (In TurboTax, this information usually is listed towards the end of your resident state tax return)
You will want to work on your non-resident state tax return first. You will then take a tax credit from your non-resident return on your resident state tax return. (Please note that you will only get a tax credit for your nonresident income taxes paid up to the amount of resident income taxes that would have been paid if the income was earned in your resident state).
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 entire answer" to view the entire attachment)
Same question but what if my ny employer only took NY taxes out of my pay. Since covid, I will have worked 3/4 of the year in NJ. I should be able to claim the ny tax rate for 1/4 and nj for 3/4 when I do my 2020 returns. But since my employer only takes my ny wages, Will I owe under payment of taxes on NJ because none were held?
....BUT as noted in the answer above.
1) (and using a "guess" as to your exact situation) ....if you physically worked in NY part of the year, and then telecommuted from you NJ home to the NY office for the rest of the year...then NY taxes all of that income...since they do assess the tax on telecommuters, and that is what your employer should be doing.
Yes...NJ will also use the same income to calculate a NJ tax (Along with any other income you have), but NJ will then allow you to take a tax credit for the taxes that you had to pay to NY (but only up-to the tax that NJ would have applied to the same income). The tax software does that calculation, but only if you do the NY non-resident tax return first....so.. Make sure you fill out your NY non-resident tax return interview before the NJ interview....but neither NY nor NJ should be done until the Federal forms are entirely filled in...every scrap.
2) IF, on the other hand, you were reassigned to an actual physical company office in NJ for the last 3/4 of the year, then yes, the company "should" only withhold NJ taxes for that 3/4ths of the year and assign the amounts appropriately.....and you need to get that straightened out with your company ASAP if they aren't doing that yet.