I am a couple of classes away from a Criminal Justice degree.
I think that people on the spectrum would have problems with this job, especially with people skills and interpersonal communication.
I think that people with Aspergers would do better with support jobs in this field such as investigator, forensics, crime mapping, etc. The sad fact is though, in many cases you have to start out as a beat cop and work your way into these fields.
Another field to take a look at is security. I know that I doesn't pay well, but I know a number of people on the spectrum who are in this line of work and absolutely enjoy it. I worked in this field for close to 10 years. I would look more at industrial security/ night watchman type position. You wouldn't have to deal with as many people as lets say a bouncer or other types of security work.