I was flipping through Do What You Are the other night. It says that SJs and SPs tend to enjoy police work. And I've noticed from various other sources that police/detective work is preferred by SJs or SPs.
Ironically, though, I would think that the ideal cops would be in NT or even NF territory.
The detectives in classic literature seem to be INTJs (Sherlock Holmes, for example). And the nature of detective work seems to be in the realm of an NT; detective work involves analytical perception, but the purpose is to derive meaning from clues.
Ideal cops and detectives are also said to have good intuitions about people, placing them in the realm of NF.
I can see SJs and SPs doing police work because of their desire for servitude and action, respectively, but is that what makes them good cops?
A Sensor's memory for acute details may help them enjoy police work. An iNtuitive's desire to understand underlying patterns would also help them enjoy police work.
With so much of both worlds in police work, I'd say that the distinguishing function is primarily J. Since the J is more willing to work in both worlds regardless of natural preferences.