Imagine, in England, UK, a human limb is found lying in the street. How long does it take for the police in UK to be at the scene to investigate the area for clues and in search of the remainder of the body? And if the dogs trace the rest of the body to a house, and there's no answer when police knock at the door, how long does it take for the police to get a warrent so they can enter the private grounds and continue their search there?

The questions I ask are in accordance to UK police procedures, as different counttries have their own procedure timescales.

You might try calling your local police station to see if there's someone who would be willing to serve as a consultant. That's what I did with one of my novels. Strangely, they seemed to be used to getting this sort of question. The officer I spoke with was very friendly and happy to answer questions. On the other hand, he did say that I made it easier for him because I had done a lot of research before calling. I was able to ask very specific questions. He also offered to let me do a ride-along, but I didn't need that for my story and felt like I would have been doing it just to be a voyeur.