Moved from NJ to NYC, still work in NJ

It depends. There are a few steps you need to take when moving and continuing to work in the former resident state.

1. You will complete part year resident for each state, New York (NY) and New Jersey (NJ).
2. NJ - will tax your income for the whole year even though part of the year you didn't live there. There is no reciprocal agreement with NY so NJ wants the tax from income you receive physically working in NJ. 
   1. When you complete the NJ return use a reasonable method to calculate the tax on only the income earned while living in NY.  That method would be to take the NJ income earned while living in NY and divide it by the total income for the year.  This will give you the percentage to multiply by the total tax liability on the NJ return.  The result will be needed on the NY tax return for the NY residency period.
3. NY - You will include the income earned during your residency period on this part year return. Only that income should be taxed on the NY return.  And because it is being taxed on NJ you will receive the following credit. Watch the screens while preparing the NY return and enter the information you calculated above (income and tax for the NY residency period reported on the NJ return).

The credit for taxes paid to another state on the same income is used on your resident state because they do not want you to pay taxes twice on the same income.  As the resident state all worldwide income must be included.

The credit for tax paid to another state on the same income will be the lesser of:

1. the tax liability actually charged by the nonresident state, OR
2. the tax liability that would have been charged by your resident state

NY tax is likely higher than NJ so you could still have a small balance due.  This will take manual intervention on your part because of the detail to your situation.