The IRS doesn't usually care whether you move every six weeks or live in one house for years. Wherever you live in the United States, federal taxes are the same. Moving between states or working in two states may, however, require you to pay income tax to two state governments. Even if you do have to fill out two sets of tax forms, though, you don't have to pay tax on the same income twice.
If you spend time in two states during the year, you can't pick which one is your real home by flipping a coin. If you have your driver's license, voting registration and car registration in one state, legally that one's your home -- your domicile, in legal-speak -- unless and until you sign up to drive and vote in another state. This can affect not only your taxes but things such as your children's right to get in-state tuition.
If you live in one state and work in another, you have to pay taxes to both governments. States with no income tax, such as Florida, are exceptions. You file a non-resident tax return with the state where you work to report whatever income you earn there. When you file in your home state, you report all your income but claim a credit for your out-of-state tax payment. Some states have reciprocal tax agreements that allow you to file tax in your home state only.
When you pull up stakes and move partway through the year, taxes are simpler. If you move from, say, Georgia to North Carolina, you pay Georgia taxes on what you earned in Georgia, and North Carolina taxes on money you make after the move. If you want to stay a Georgia resident because it's a better tax deal, you have to avoid making any of the changes that would shift your domicile to North Carolina.
Military members are a special case. It doesn't matter which state you're stationed in: you only have to file one tax return, and that's with the state where you're domiciled. Another special case is when you move to a new state to take a new job. If it's at least 50 miles further from your home than your old job, you may qualify to write off your moving expenses from your income taxes. The state you move to may allow you to write off moving costs too.
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