If you live in one state and work in another state; that income is subject to taxation by both states. This is how it works. You file a nonresident return for the state you worked in, reporting only the income you earned there.
You report all your income on your resident state return, including the income earned in the other state. Your home state calculates tax on all your income, but gives you a credit, or partial credit, for tax you paid to the other state.
When you live in a state without an income tax (e.g. Texas), there will be no credit, since there was no Texas tax. In other words, having legal residence in a state without an income tax does not get you out of paying state tax on that income, to the state you worked in.
