This sort of thing has all sorts of fun wrinkles. Around here, NE Washington, there are lots of people who live in Idaho (Income tax) but work in Washington (no income tax, probably never will be[1]) which leads to fun. Of course if you live here and buy something in Idaho, where sales tax is much lower, you are supposed to report it and pay the difference.
When the Trust Fund my late mother set up sends me money (every other Blue Moon) I owe no Iowa Income Tax because I do not reside in Iowa and none of the Trusts income has an Iowa source[2]. There's even a special schedule to file with Iowa tax forms to account for all this.
So every situation is different, depending on states involved and source of the income. See an accountant in the area for exact (and very boring!) details.
Hank
[1] would require an amendment to the state constitution, highly unlikely to pass. I'll hold my opinion on that.
[2] the trustee goofs up on this with great regularity. That's what happens when you send an Attorney to do an Accountant's job! Of course he seems to like paying income tax, every year he sends a bundle to Uncle Sam that would not have to be paid if he passed the income through to me. (my marginal rates are lower)