Generally you need to file a resident return in the state where you are a permanent resident. This state has the right to tax ALL of your income, wherever it was earned.
After you file your resident return in your home state, you then need to go about filing a nonresident return in every other state where you earned money. A nonresident return only taxes you on the money you earned in that state. What often happens is that you withhold some income for each state tax.
Let’s take a real-world example.
Let’s say you live in Colorado and you own an income producing property in Ohio. Come tax time, you would need to file a resident return in Colorado (reporting all of your income) and a nonresident return in Ohio (reporting only the income you earned in OH). Worried about being double-taxed? Don’t be. You will have an opportunity to claim a credit for taxes paid to the nonresident state. They will then divide whatever has been withheld between them and the state whose tax liability was not exactly met will either give you a refund or a tax bill.
We are not tax advisors nor accountants. The above statements are tended to be for discussion purposes only. Please seek professional tax advice from before making any decisions.