Louise, I may be way off base here but is Beagle the killer??
no... that would be too soap opera. If you are looking for the "big picture" on this murder and what it means in the overall scheme, it is to bring back to Ellery some of the emotions of his college relationship and its turmoil, as well as the recent events with his being shot at, which is still sinking in.
I did some research on violent crime in Laramie, and there are about 30 homicides per year (just over two a month) and they were due for one, statistically. Over half of those are by gunshot.