Generally speaking, serial killers aren't likely anywhere, but you know.
I suppose it's possible, but it's not particularly likely in the case that you described. If there are morals involved (ie, the urge to punish the criminals), the officer is not likely to be able to double cross those, as that would make him a criminal as well.
Plus, the setting of a self-defense shooting would eventually become suspicious. Internal Affairs investigates all of those, and the public can get quite rowdy about them as well. It would fall apart sooner or later.
However, cops can certainly be serial killers (just as much as anyone else, at any rate) in other scenarios. There's the retired one here that's suspected of killing two of his wives, possibly more; that would count.
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