I found a video that shows what happened to me:
I was walking around doing my own thing, when a random civilian pulled a gun, shot 3 or 4 other civilians, and started running. I pursued a few blocks and finally got the takedown.
The police had been called (presumably by someone after the shooting, and I heard their sirens as I chased the guy down). After I got the takedown I waited around to see if they would give me a nod or something... sometimes games have cool little things like that in them, and I enjoy finding them.
Anyway, the police showed up and started shooting me and killed me. Why did they do that? How come they don't do that when I take down other criminals?