They'd have to pay for the cost to correct this (fix it) IF you can show with medical evidence (such as the testimony of another dentist who examines you) that it fell out because they did an inappropriate procedure or did sloppy or careless work. But if they did an appropriate procedure and did the work within accepted standards but the crown fell out for other reasons, they would not be liable. The law does not assume they were at fault because a crown fell out within 3 weeks; you *must* have medical evidence of fault (which can be expensive; you'd have to pay the dentist or other dental expert for his/her time and work) to show fault in order to successfully sue. And even if they *should* fix it for free, the only way to force them to do so if they refuse is by suing and win: there is no other or mechanism to compel them to do this.