Yes. What states? Some states have reciprocity which means wages are taxed only by your resident state. You might need to file two state returns if there is. A nonresident state return to get back any withholding for that state; no withholding - no filing unless you earned other income in that state. A resident state return to pay taxes on all wages earned in the other state. Another key factor is to do the nonresident state first. if there is no reciprocity, your resident state uses the tax likability (not the taxes paid) to compute a tax credit to minimize or eliminate the double taxation.
