Can an aspiring author shadow people to gain research for their novel?

[CassieCharisma]

You see shows like Castle where the novelist is allowed to shadow Police Detectives to gain research for their novel. To gain first hand experience of murder scenes, Investigations, interrogations, arrests, suspects, linking all the clues together to give the victim justice, some experience in the medical examiner department when they run autopsies and tests on the deceased bodies, etc.

So, what I'm getting at is, after seeing this show and hearing that other authors do it too. Can any person who wants to write a novel shadow the police force, doctors, whomever they need to gain the research for their novel? And if so, how do they go about being able to do so?