Not sure if Bladerunner itself since i haven't tried it yet, but the mutant year zero engine (the one that Free League uses for most of their games with the ocassional mechanic thats for the setting itself) in general might be perfect for this.
>Not to little, not to many skills and attributes.
>Can roll new characters pretty fast in case of death
>Critical wounds mechanic that makes combat to gruesome if you get hit.
>Mental sanity mechanics
If not, i think Delta Green might work well for Psycho Pass.
In any case, you would still have to come up with the stats for a Dominator with its three phases, plus the Shotgun experimental Dominator.
It would be overpowered as hell thou.
In the case that you actually want to run a Psychopass game outside of Japan, check Free Leagues Twilight 2k.
All you would have to do is besides making the stats for the dominator is skipping rolling for rads, and thats it.
The character creation is pretty decent too, pretty similar to Cyberpunk 2020s where you can roll for your general formation to get better stats and specializations.