They've got markings, but they're those low visibility types.
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That's not one of our guys. He's from a town over. The town picks up what cars they can, usually hand me downs from other departments. Our police force consists of two officers, each drives a car that is low visibility marked from two different towns. They haven't bothered to repaint or decal them.
My city has gone to those low visability marking on police vehicles just like those ones. The spotlight on the driver's side still gives them away.
Anyway, odds are your local area doesn't have a coroner. Ours get shipped off to one of the couple state medical examiners offices so it usually take about a week o get the remains back from a murder.
For whatever it is worth, there was a several hour hostage situation literally a few hundred feet from my property and I had no idea until the next day when it was the headline in the paper. I was home the entire time it was going down and was in and out of the house so you would think I would have noticed, but nope. LOL.