which irs form to use to file for living in nj but work in ny

No - as long as you live and work in the US the IRS doesn't really care what state(s) are involved. However, it IS important to understand the consequences of living and working in different states at the state income tax level. So I wonder if you may actually have a question regarding how the states of NJ and NY handle your situation? In brief, there are no reciprocity agreements between NJ and NY, so you must file tax returns with both states. First you figure your NY income tax which is based on the wages you earned while physically working in NY State. Then you calculate NJ taxes based on total income you made while living in NJ - this includes the wages from your NY job as well as any other income such as dividends, capital gains, etc. The good news is that when completing your NJ tax return you can take a credit for "taxes paid to other juruisdictions," namely NY in your case. The result is that you effectively end up owing close to $0 to NJ on the wages you earned in NY. I hope this is reasonably clear - post back if you need furtgher details.