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Don’t ever hand your phone to the cops
(www.theverge.com)
This is a most excellent place for technology news and articles.
They can't detain you in the US for the purpose of conducting an investigation
They can in a few states. Delaware, for instance, where the law provides them two hours even without having to clear the bar of reasonable suspicion. This is of couse blatantly unconstitutional, but it's still a state law.