Have hospital doctors treated you differently if you came in with a self inflicted injury?

If you come into the ER with self inflicted wounds, like slit wrists or something, they may suggest to your family, or make it mandatory that you stay inpatient for monitoring. Just to make sure you won't go finish the job. It's a liability thing. And insurance may not pay for your ER visit if you do not follow through with doctors orders. Just so you know.