Hi - I live in NJ but trained in CA for 5 months between May and Sept. Because it was not determined whether I needed to stay in CA after the 4 month period, my employer considered me a CA resident for the entire year, even though I maintained permanent residence in NJ. How do I handle the dual tax status - pay CA first - but only for the 4 months? Then take a credit in NJ for 4 months payment in NJ?? Also, CA will owe me money - do they even have any?? This is too confusing! Thanks! K

Report income from May to Sept to CA. From Sept to Dec it is NJ income.
Read: Your U.S. Tax Return: Working or Living in Two or More states

To add to what Mukata said - for both CA and NJ you file as a part-year resident. You will have to report all income for the year to both CA and NJ and initially calculate taxes as if they were going to tax you on all income, but then you multiply that by a percentage representing the portion of the year you spent in each state.