In this case, your therapist convinced police to see to it that you were transported to an emergency room for an evaluation. Any citizen can potentially do that. If you call a crisis "hotline," the counselor or volunteer at the other end of the line can call police and get the same result. That happened to me once. The paramedics are there to actually transport you safely, but the cops are there to see to it that you cooperate with the paramedics. Sometimes, police will simply transport you themselves, though they prefer to let healthcare personnel do that.

Once in the emergency room, it is the emergency room physician who makes the actual decision about whether or not to order that you be hospitalized. That doctor will be very interested in knowing what caused the therapist to call the police. That doctor will get that information from the accompanying police officers. No therapist out in the community has "admitting privileges" at any local hospitals. Emergency rooms often have clinical social workers on staff or on call, who can perform psych evals and give their impression to the E.R. physician. Specially trained "psych nurses" also sometimes perform this function.

I'm not trying to split hairs with anyone. The O.P. seems interested in knowing who has exactly what legal authority to do what. It just so happens I was in position to learn that. In my own case, when the cops and paramedics took me to the psych hospital, the doctors there didn't think I needed to be admitted, despite the counselor conveying very serious concerns. I had to talk them into keeping me. They did - for just 23 hours.