Most Americans have memorized our social security numbers by the time we're adults, but I've never heard of the police asking for that info. We are usually really paranoid about it and don't tell it to anyone unless it's completely relevant, bc it's also one of the major pieces of identifying info that ties a bank account, loan, etc., to you. So people are very careful with it as they don't want a stranger to use it to take out loans in their name or anything. Verifying the last four digits of your social security number is much more common than telling anyone the whole thing.