If your resident state collects income tax, you’re still required to pay taxes to your resident state on any income that was earned in a "tax-free" state. You cannot avoid state income taxes simply by working in a tax-free state. You have to also be a resident of that state.
Similarly, if you are a resident of a tax-free state, and have worked in a taxing state, you still have to pay taxes to the state where you worked. Unless you are working in a reciprocal state, you will have to pay taxes to the state where you earned your income. You would file a nonresident return to pay these taxes.