Can they force you to give up the post-it on which you wrote down your password? If yes, are there any real limits to how much pressure they can apply before they give up? If no, what's stopping them from giving you a pencil and a stack of post-its, and letting you know they'll keep applying pressure until you produce a post-it with the password on it, which they "know" you have "somewhere"?
Point being, I feel this is getting into xkcd://538 territory.
Depends. If you have the resources to hire a lawyer, then what you describe is governmental overreach borderline on torture that will lead to the government paying out to you when you sue them and plenty of government employees being reprimanded or fired. If you do not have these resources and end up before unscrupulous law enforcement, you might very well have your rights abused until a journalist or the ACLU or some other equivalent decides to fight for you.
Point being, I feel this is getting into xkcd://538 territory.