I have two W-2's, one from NJ company - worked there from Jan - Nov; one from NY company... worked there in December.

Resident of NJ from Jan - Sept
Resident of NY from Oct-Dec

What state tax do I file for? Can I file for both of them separately?

Step 1 - fill out the NJ tax form NJ-1040 for the period you were a resident (Jan - Sep).

Step 2 fill out a NJ non-resident form NJ-1040NR for the two months you were not a resident but earned income in NJ.

Step 3 - fill out NY state tax form for part year resident (IT-203) for period of Oct - Dec, reporting all income during that time. You then take a credit for the taxes paid to NJ during the period you lived in NY.