It is very suspicious, that given her mental state, they did not have her admitted to hospital on a 5150: danger to self/danger to others.
It is suspicious but I don’t believe some police officer at that station killed her. I think she left, was walking around and fell off the cliff. It was negligence by the police but I don’t believe anyone there murdered her.
Maybe they didn’t think she was mentally disturbed. Maybe they just thought she was just trying to get out of paying for her meal by acting crazy.