So he isn't dead?
I know all this stuff goes crazy and tempers get moving etc in a manhunt like this but I always get angry when cops kill a suspect that could be caught and we could actually find out what actually went down for sure. Basically supressing fire until he holes himself up somewhere. If he takes a hostage sure, pop him in the head and keep the hostage alive. If not you try to corner him and hope he runs out of bullets so he doesn't kill himself and then you wait him out and take him into custody and start some questioning.