The novel that this is based off of explains why the Predator didn't kill the cop. Predators come from a society that is very Klingonish about honor. It surrounds them... nay, rules their very existance. Predators will not fight with weapons when they are facing someone who is unarmed, and also won't kill women. They have the utmost respect for the human race though because of our ingenuity and due to how brave we are in the face of danger. Some might run, but there are always people who will stand up and defend themselves.
In the novel, the Predators use hunting the Aliens to be a "right of passage". That's how they gain honor in their clans, and also how they ascend to a higher position. The novel takes place in the future though.
There you have it folks, that's the way the Predator operates.
I also added "Spoilers" to the outside of the thread.