Police helicopters do not carry medical staff on board! Although police crews are trained in first aid, it is not their primary role and sometimes it's better to let more highly qualified and experienced medics look after the patient.
Sometimes difficult decisions do have to be made. We were once called to a serious road accident. I had to insist that a particular badly injured accident victim was not loaded onto 'my' police helicopter after all, but taken by road ambulance instead. It made me quite unpopular at the time but it was the correct decision to make. Reason? The ambulance was already on scene, as were two doctors who happened to be driving past and had stopped to help. The patient was undergoing treatment to keep open his airway and also CPR. Once he was in the helicopter, due to space constraints there was no way to reach him to continue the treatment (we had already removed the co-pilot's seat to fit a stretcher in; the aircraft was not designed as a casevac aircraft, it was a police observation fit). In my opinion he would have been put at greater risk than by enduring a road journey.
Things got quite frosty (especially with the fireman who had to carry him back across the field - he was an unusually large patient). Once I explained the situation to the doctors they agreed with me. The patient survived.