I worked in NJ but by company has w2 address in MA. Also, they had state tax deduction for MA. Do i need to file state tax for MA? I am filing as NJ resident.

Yes. You will have to file a Massachusetts income tax return if you had MA tax withheld from your pay:

1. Either your company made a mistake—in that case you will file to get back tax that should not have been withheld; or
2. You have to pay MA tax.

It seems like a mistake. Massachusetts is taxing nonresidents who worked in MA prior to the pandemic but are now working from home. If that's you, then you have to pay MA tax. You can claim a credit on your New Jersey return for tax paid to MA.

 

Otherwise you can file a MA return to get back your withholding. TurboTax will show you the types of federal income you have and a box for "Non-MA." All your income should be "Non-MA" making your MA income is $0. 

 

Mail your MA return and attach an unsigned copy of your NJ return with a note explaining that your company take out MA tax by mistake.

 

 

Massachusetts says:

 

Pursuant to the regulation, for the duration of the Massachusetts COVID-19 state of emergency, all compensation received for personal services performed by a non-resident who, immediately prior to the Massachusetts COVID-19 state of emergency, was an employee engaged in performing such services in Massachusetts, and who, during such emergency, is performing such services from a location outside Massachusetts due solely to the Massachusetts COVID-19 state of emergency, will continue to be treated as Massachusetts source income subject to  personal income tax under M.G.L. c. 62 and personal income tax withholding. 

 

TIR 20-5: Massachusetts Tax Implications of an Employee Working Remotely due to the COVID-19 Pandemic