Q. Do they need to file a federal tax return if the amount is under the federal standard deduction?
A. No. But, at your other post, you indicated you are using the "loop hole" to claim the tuition Credit. If you add another $4000 of taxable scholarship to their income, they would have to file.
Q. Do they need to file a NJ state tax return?
A. Yes.
Q. Since I don't receive an education credit for them, would it make more sense for them to file separately (as a non-dependent)?
A. No. They are not eligible for the refundable credit*. And there is no net taxable income (so, no tax) to take a credit against.
Q. Is seems like we would save around $250.
A. I don't see how.
Q. Are they now a resident of NY?
A. No, not even if the summer job was in NY. But they may have to file a NY non resident return, as well as a NJ resident return.
*While technically there is a provision that allows your student-dependent to claim a federal tuition credit, from a practical matter it seldom works out. A full time student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)
