In the perfect world, the police helicopter would be staffed by a police officer pilot and police TFO's - the end!
In reality anyone who qualified as a civvy pilot wouldn't be working as a police officer on police officer wages, I would suggest, especially after slogging their guts out to do CPL/IR exams!! And so - a civvy pilot is required to fly the police helicopter.
TFO's - a thorny issue, but an all civilian crew could also do the job. Provided they were trained and capable in the first instance, they could do the job of a police officer in carrying out the role of a TFO. Now I know this is a very very thorny issue (having lived thru it for many years), but I know it works because I did trials involving paramedics doing the role of TFO's and the person in question was exceptionally good at doing it. Head and shoulders above the average police TFO.
NOW - for political and motivational reasons, police officers currently carry out the responsibilities of the TFO.
In answer to your direct question old pilot: The pilot alone cannot do both jobs (fly and TFO) too much work - massive overload, flt safety blah blah. There is an incontrovertible requirement to instal atleast one other on board to systems manage. Whoever does the job of a TFO, MUST know what they are doing, they must have good communication skills, must have adequate SA capabilities and must be competent IT operators. They should also be familiar with police procedures. It so happens that police officers (easily capable of responding to the above) are employed for the reasons given earlier.
The suggestion that ONLY police officers can do the job because of their 'savvy nature' is a myth as our trial proved outright.
OldPilot - be not surprised to learn that TFO's are a very competent and necessary essential in airborne police ops.