Can two states both tax the same income, and how do I avoid double taxation?

Yes, it's possible for your resident state and the state where you earned income to both claim it, but most states prevent true double taxation through a credit for taxes paid to other states. Typically your home (resident) state taxes all your income, then gives you a credit for tax paid to the nonresident state where the income was earned, up to your home-state rate. The Supreme Court's 2015 Comptroller v. Wynne decision reinforced that states must provide such relief. Problems arise when the two states disagree about residency, or when local taxes aren't covered by the credit. If you moved or worked across state lines, file both a resident and a nonresident return and claim the other-state credit. A tax pro can confirm which state gets first claim.