You have a constitutional right to freedom, and unless they believe you're a harm to yourself or others they must release you whenever you request. However, I don't know the specifics of your state, but in most states they have a right to hold you for up to 72 hours for observation. After this point they must release you, or initiate civil commitment proceedings in court, typically in front of a magistrate, justice of the peace, or associate level judge. If this has not happened and you feel you're being unjustly held, you can file a writ of habeas corpus. Simply write on some paper: this is a writ of habeas corpus, I wish to be brought before the court of this jurisdiction as soon as possible; have yourself and a witness sign and date it, then hand it to your doctor. If they continue to hold you after this point you may have a right to bring a tort claim against them for damages in court, as this would now constitute false imprisonment. Even if you have signed yourself in voluntarily you still have a right to be release whenever you want, you simply sign yourself out.

This has happened to me, the last time it was because I had good insurance. They kept on saying I was sick and needed to stay another day, until one day the hospital administrator said my insurance was refusing to pay for further treatments. She proclaimed I was, magically, heeled and told me to vacate the room before 5pm, or I would be charged for another day. It's a game to them.

Each state is a little different regarding civil commitment procedures, you'll have to google the details. Generally its bad to be involuntarily committed, because you loose the right to govern yourself at that point, on the other hand the state, county, or city usually picks up part of the tab if they commit you. Whatever happens, remember you're in a psychiatric hospital, they can strip you naked, strap your *** down on a table, and inject you full of haldol if you become violent with them. You're best course of action is to simply document all of your requests and then talk to an attorney once they let you out.