Yes, tax returns will be required for both states, but his resident state should provide a credit for taxes paid to the non-resident state.
Living in a
particular state only for the purpose of attending school, or completing an internship, probably will not
establish residency in that state. You may still have to file a tax return in
that state if you have taxable income there, but you would file as a
non-resident.
Residency is based
on the concept of domicile. Your domicile is the place where you have family
connections, lived and/or worked, belong to a house of worship, and, most
importantly, the place to which you intend to return after you have been
away. Once you have domicile somewhere, it remains until you move away and abandon the intent to return.
So, if your son's domicile is the state that he moved from to attend school or take the internship offer, and he intends to return
there, barring future events (such as a post-internship job offer), then that
state is still his domicile, and is the place where you are a resident for tax
purposes.
