I'm so sorry you had to endure that. Did that friend know you had a therapist? In her place, I would have asked that question and encouraged you to reach out to your therapist. If I was really concerned you were suicidal, it would be me on your doorstep, not the cops. And, I'd be trying to reach your therapist myself, if it came to that.
Our society must radically rethink how we approach mental health – especially for mental health calls. It should almost never be the police who respond – that stygmatizes the one suffering and makes them feel criminalized. Sadly, is someone calls 9-1-1, police will be who are sent. We need mental health crisis response teams. At the least, a mental health professional should be embedded with police on such calls – that would be the weakest least we could do.