How to start an interfacility transfer between hospitals? (Transfer patient hospitals)?

I need to move my mother to a different hospital but I dont know what my options are. She is not in a condition where I can just put her in my car and drive her to the new hospital so she would need an ambulance. The hospital is not very far and is about 10 minutes driving distance. Do I call the new hospital first and tell them contact the current hospital? If so what department in a hospital usually handles cases like these? Thanks