By city ordinance, CSFD is in command of all "medical scenes" and AMR Pikes Peak region is responsible for all transport to the hospital. Fire has 20 ALS engines and six trucks and a heavy rescue that are often also ALS. AMR averages about 14 units posted during the day in SSM. Fire is usually there first, and they'll get a history and any other treatment if indicated since unless the ambulance pulls up with them they don't generally get an ETA from AMR, only where the ambulance is responding from. Fire will also if possible move the patient to stretcher accessible area (they have those rescue seat stair chairs).
Usually considering that the AMR medic is soon in behind, they are doing most of he patient care and fire seems happy to let them so they can clear. I've never seen a fire medic jump in the back of the ambulance without invite or anything like that, nor are medics permitted to leave the scene without the AMR medic's ok. The only strange part of the working relationship is fire being in control of the patient while the AMR medic has a broader scope (RSI and a few other things) and their medical direction comes from different hospitals. Fire also has two ambulances stationed in high call volume areas but rarely actually transports with them. The "new" AMR trucks with the fancy paint were tested here and have been around for there's years so they have a nice fleet.
I don't work directly for either agency, but rather an organization that has some EMS first response responsibilities and am good friends with a few AMR medics as well as some fire officers and training division members.