When moved during the year, How to prorate income for the state tax returns?

[miamia]

Hi, My timeline:

I was living in NJ.
Graduated in April.

Start work in May ( start earning and get relocation money and sign on bonus)

MOVE to WA in July.

For NJ tax return, turbotax ask me about how much I earned while living in NJ. My question is:
1. For the relocation and signon bonus, should I split it like 3/7 for NJ ( because i worked for the comapy for 7 monthes last year and 3 month happened in NJ)? Or should the whole amount of relocation and signon bonus be for NJ tax return?

2. should I just report all the salary paid to me through May to July for  NJ? Or should I also prorated the July part ( as I moved and lived in WA in July)

Thank you.

[ErnieS0]

Does your W-2 show New Jersey wages in Box 16? If so, your company probably split your income the right way.

New Jersey residents are taxed on income they earned while living in the state. Your relocation and signing bonus, if received as a lump sum, should all go to New Jersey.

July should be prorated based on where you were living when you got paid. You can refer to the year-to-date earning on your pay stubs, although those may include non-taxable income.

Washington state has no income tax so you will only have to file a part-year New Jersey tax return.

[miamia]

Thanks, ErnieS0!

Does it matter if the box16 number is different from the accurate amount earned in May-July?

Details:
I found that my box 16 is more than all the income from May- July. I think it is because I forgot to update my home address until Sep. I asked my payroll to fix the W2 last week but they just replied that they withhold based on the system's address, and would not change the W2.

[DMarkM1]

No, it's okay if the box 16 amount is not correct.  You should prorate correctly based on where you lived.  As @ErnieS0 stated the sign on bonus and relocation should be NJ since that is where you were when earned.