Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington, and Wyoming don't have income tax. If you're a resident of one of these states, you don't need to file a return in that state.
New Hampshire residents only file a tax return if their interest and dividend income (not wages, earnings, or other income) exceeds $2,400 ($4,800 for joint filers) plus additional exemptions for age, blindness, and disability.
If you're a resident of a state with income tax and you earned income in a tax-free state, you need to report that income on your resident state return.
For example, if you're a California resident and worked in tax-free Texas, you'd still have to report your Texas earnings on your California return as well as your federal return.
Similarly, if you're a resident of tax-free Texas and earned money in California, you'd have to file a nonresident California return to report your earnings, and you'd report those on your federal return as well.