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A United States citizen is not an alien in American Samoa, but nonetheless can be a tourist or business person and is subject to the 30-day limit (extendable).
41.0202 (1) (t) βTouristβ means a person visiting American Samoa for the purposes of sightseeing, who intends to remain in American Samoa less than 30 days and who has a residence in the United States or a foreign country which he has no intention of abandoning, and who is visiting American Samoa temporarily for business or pleasure.
(3) A tourist or business person must:
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(D) a tourist or business person may stay up to 30 days and with approval of the Attorney General or his designee may stay an additional 30 days; however, the filing of an application for an alien registration card pursuant to 41.0303 shall not entitle an alien arriving in American Samoa under subsection (D) to extensions of stay beyond 60 days after original entry into the Territory.
Violation of the law can be a misdemeanor and subject the offender to deportation:
41.0615 Except as otherwise provided in this title, the following classes of persons not permanent residents are excluded from admission into American Samoa and are subject to deportation:
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(22) persons who have violated any provision of this title or regulation of the Board, in addition to any other penalty which may be imposed under any provision of the law;
41.0708 (a) A person commits the crime of illegal presence if he is present in American Samoa knowingly in violation of the immigration laws of American Samoa.
(b) Illegal presence is a class A misdemeanor.
Of course, permanent resident here means a person entitled to permanent residence under American Samoan law (not a U.S. LPR under federal law).