I'm not a cop so I can't say what they find most useful in a detective, but my guess is that the internal filtering process will select for the most intelligent

I'm not a cop so I can't say what they find most useful in a detective, but my guess is that the internal filtering process will select for the most intelligent of the ones they have recruited, and that a lot of that intelligence is defined in terms that are specific to being a cop, and specific to what they learned while already being a cop, so it may not be an innate intelligence that is optimal for the kind of person you want to be a detective. Personally, I'm all for very intelligent cops, and at the very least, having lots of people on the spectrum of intelligence in various roles makes sense to me.