Should The Hospital Have Discharged My Dad When He Told Them That He’d Kill Himself If The My Did?

I am in California, but this takes place in Arizona . On 7/17/26 my dad was brought to a hospital in Prescott AZ by police at 2pm and he left at 3pm against medical advice. He then made his way to his (deceased) mothers home where one of his sisters resides, the home is in probate and all the surviving children have claim to the property (he and that sister are both in Arizona while one lives in California.) my dad begs to be able to come inside, she says no, calls the police and he leaves before the cops arrive. They eventually locate him and he is then taken back to the same hospital he had been taken to earlier. This is around 6pm-7pm on 7/17/26. He has had back surgery years ago, it’s been causing him issues and pain, and has had to use a walker. He doesn’t have a vehicle and was getting to and from on foot with a small suitcase on wheels. While he was admitted in the hospital, he had told staff that he would kill himself is he was discharged. At 4:30 am 7/18/26 he was discharged anyways. He was brought back to that same hospital at 7:15a (that’s the time he was admitted) 7/18/26 after being found in front of a cvs, under the carport, which has video surveillance of him being there for 2 hours furring monsoon weather, committed suicide. The officer who brought my father’s belongings in himself to the hospital following the ambulance, it’s noted in the report by a nurse- “he said he would do that.” He was breathing but unconscious, Bc that hospital isn’t equipped to handle that type of situation, he was transported to another hospital an hour awayto undergo surgery at a trauma center. When paramedics had originally found him, they had attempted cpr for 30 minutes, based on neurological test results it was decided best to choose comfort and let him go. He was a donor so they kept him on a ventilator for organ testing to see if any organs were viable for donation. I’m trying to wrap my brain around why this was allowed to happen. I now have the cause of death and it is suicide, by multiple lacerations, no other contributed factors; he cut his wrist. If this were a movie/documentary I’d be screaming at the tv like this is not okay!
Location: I am in California