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The thorny topic of offshore tax havens took center stage recently when Apple CEO Tim Cook was grilled by U.S. senators about the company’s tax-minimizing maneuvers. While many wealthy individuals take advantage of exotic locales to shelter income, a far more common tactic is to move from one U.S. state to another. Such a move can pay off nicely, but caution is warranted: The price you pay for any missteps could far outstrip the tax savings.

Tax rates around the U.S. vary widely. At the high end is California, with a top marginal income tax rate of 13.3%. New Jersey, New York, and a handful of other states have top marginal rates in excess of 8%. At the other extreme, seven states — including Florida, Nevada, and Texas — do not collect any personal income taxes from their residents.

Moving your residency away from a high-tax state entails a slew of requirements. While you can still maintain a home in your former state, you can usually spend no more than 183 days a year there, or you’ll be deemed to have never left. You’ll also need to show that you’re spending more time in your new home than the old one. For example, spending three months a year in your new Florida condo, five months in your old New York home, and four months traveling in Europe won’t cut it with the State of New York. Auditors will even look at your insurance policies to see where you’re storing your most valuable items. “It’s not just about counting up the days — it’s about your entire lifestyle,” says Timothy Noonan, a tax attorney at Hodgson Russ in New York City.

You’ll also have to break many ties with your old state, including transferring your bank accounts to your new state of residence, obtaining a new driver’s license and registering to vote in the new state, and revising your will and other legal documents. If you don’t meet all those requirements, you’ll be slapped with a bill for back income taxes from your old state, plus penalties that can hit 25% of the taxes owed and interest. You could even face criminal charges. “The consequences if you don’t do it right could be dire,” says Noonan.

What if you move to another country seeking tax relief? You’ll have to file a federal tax return each year if you maintain your U.S. citizenship, but exemptions and foreign tax credits will probably reduce your payment. Certain states, like California and Virginia, are more likely than others to continue levying state taxes on your worldwide income. U.S. retirees who move abroad forfeit their eligibility for Medicare, but most will continue to receive Social Security payments. Whether you’re considering the Cayman Islands or Key West, be sure to consult a tax adviser before taking the leap.

A former compensation consultant, Janice Revell has been writing about personal finance since 2000.

This story is from the July 1, 2013 issue of Fortune.