Returning to the scene of the crime

I would say yes it is, particularly with regard to arsonists. They like to see the results of what they've done.

And I've often heard those in law enforcement say they look at any crowds that gather to see if there's anyone acting suspiciously.

Murderers can return to dump sites to eradicate evidence as in the case of the Yorkshire Ripper who tried to retrieve a five pound note which could have identified him, or to further mutilate a body, or to move it into the open to ensure its discovery.

Serial Arsonists do, usually right in crowd and get off on watching fireman and place burn.

Occasionally murderers will visit grave of their victim on anniversary of murder.

Rapists very rarely although they will take a 'trophy' from scene to fantasize.
ETA: according to my hubby, police commander--

It depends on the crime and criminal. Yes, arsonists are notorious for this. They want to watch it burn.

Most others, not so much. Murderers do occasionally. Some like to watch the police work the scene.