Totally depends on the circumstances and a lot of factors. A medical hold is not necessarily going to happen at all. From personal experiences: at a semi-private school, person did the attempt to jump off a roof. Was pulled down by a friend. School officials called the parents, no police or anything. Made the student leave the school, and that was it.
Adult who overdosed on sleeping pills. Taken by ambulance to a hospital and stomach was pumped. A psychiatrist spoke with them, decided they were no longer a danger to themselves, and released. Had they not felt it was safe, had told patient's friend they would hold 24 hours at most for observation.
Lot of factors come into place, including location, circumstances, etc. Quite honestly, though, far more attempters have no reprecussions or anything else - they are stopped by someone and live goes on. Its only if someone gets involved like the cops or a hospital that there is even a chance of something more happen. So depends on the circumstances in your story.