After the bank performs CIP, it has an identifying number for the individual. If it's foreign, you know he or she is not a U.S. citizen. Ironically, if it's a U.S. TIN, the individual's status is ambiguous.
You must ask.
In my opinion, the most important due diligence question is "In what country are you a citizen?" If the person is a citizen of a foreign country, but a legal resident of the U.S. you will know that because, as stated above, he or she has a green card. Without a green card, a citizen of a foreign country is a non resident alien in the U.S..
TIN compliance is like 3 dimensional chess; you must be able to see and contemplate multiple boards at the same time; i.e. the Bank Secrecy Act, the Internal Revenue Code, and a tiny piece of the U.S. laws relating to citizenship.
One byproduct of TIN compliance is your institution's ability to identify (produce a list if requested) your "non resident aliens and foreign individuals." That includes resident aliens and non resident aliens.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.