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IRS.gov Website
Publication 519
taxmap/pubs/p519-015.htm#en_us_publink1000222365

Interrupted Period
of Residence(p21)

rule
You are subject to tax under a special rule if you interrupt your period of U.S. residence with a period of nonresidence. The special rule applies if you meet all of the following conditions.
  1. You were a U.S. resident for a period that includes at least 3 consecutive calendar years.
  2. You were a U.S. resident for at least 183 days in each of those years.
  3. You ceased to be treated as a U.S. resident.
  4. You then again became a U.S. resident before the end of the third calendar year after the end of the period described in (1) above.
Under this special rule, you are subject to tax on your U.S. source gross income and gains on a net basis at the graduated rates applicable to individuals (with allowable deductions) for the period you were a nonresident alien, unless you would be subject to a higher tax under the 30% tax (discussed earlier) on income not connected with a U.S. trade or business. For information on how to figure the special tax, see How To Figure the Expatriation Tax (If You Expatriated Before June 17, 2008) under Expatriation Tax, below.
taxmap/pubs/p519-015.htm#en_us_publink1000222366

Example.(p22)

John Willow, a citizen of New Zealand, entered the United States on April 1, 2008, as a lawful permanent resident. On August 1, 2010, John ceased to be a lawful permanent resident and returned to New Zealand. During his period of residence, he was present in the United States for at least 183 days in each of three consecutive years (2008, 2009, and 2010). He returned to the United States on October 5, 2013, as a lawful permanent resident. He became a resident before the close of the third calendar year (2013) beginning after the end of his first period of residence (August 1, 2010). Therefore, he is subject to tax under the special rule for the period of nonresidence (August 2, 2010, through October 4, 2013) if it is more than the tax that would normally apply to him as a nonresident alien.
taxmap/pubs/p519-015.htm#en_us_publink1000222367

Reporting requirements.(p22)

rule
If you are subject to this tax for any year in the period you were a nonresident alien, you must file Form 1040NR for that year. The return is due by the due date (including extensions) for filing your U.S. income tax return for the year that you again become a U.S. resident. If you already filed returns for that period, you must file amended returns. You must attach a statement to your return that identifies the source of all of your U.S. and foreign gross income and the items of income subject to this special rule.