Depression Support Group
Depression is a real and debilitating condition that is often misunderstood by family and friends. Its meaning can range from a prolonged period of sadness to an actual mental illness with specific symptoms. Find and share experiences with others who are going through the same struggles.
I can't believe that the police dumped her on your porch like that. If they did, SAME ON THEM! Is it possible that she lied to them and said that she was living with you?
Work with your network of friends and people you know, is there a connection that gets you to a police officer who will interact with you as a "friend of a friend"? If so then that person may be able to tell you the best way to go forward.
If you are not family, and do not have any POA over her then it is not likely that you have the option do get her committed against her will. Do you know any of her family? That may be another path for you.
Gentle hugs