The police of Sunnydale are deeply stupid
As the esteemed Mr. Snyder pointed out in "Becoming Part 2", the Sunnydale PD are just idiots. I re-watched "Becoming" tonight and, man, that episode is the absolute apex of both uselessness and stupidity.
I mean, from start to finish, they're just terrible. First, the cop that fires at Buffy while she's running away? You'd be in deep sh** for that. No cop would ever, EVER do that. An unarmed, teenager is running away and you shoot her? No way, doesn't matter what you think she's done.
And whoever is running the investigation into Buffy should be canned. I mean, okay, she gets away. But then she proceeds to go to the hospital where all the people at the crime scene are, goes back to the crime scene, then goes home, and then runs away via the bus station. You're telling me the police have none of those places covered? Really?
As a great (or at least greatly entertaining one) once said: "The police of Sunnydale are deeply stupid".