Threatening suicide doesn't fall into an unprotected category of speech (though feminist would have us think otherwise), unless say you have certain things strapped to a vest in which case they'd certainly be an imminent threat to themselves and/or others. If they happened demonstrate more than just a suicidal threat, a person may petition the courts to initiate civil commitment procedures. If the court finds they meet the criteria for that particular state then it is off to the funny farm they go.