I'd believe that the manner in which he "stumbled" onto the case would have a lot to do with it.
In our city, the cases that come in are assigned to the next detective up for a case. In Homicides after business hours, there will be a team of detectives on call for the next homicide.
If a detective makes the scene prior to it being reported or assigned for some reason, he might be assigned the case. But there would have to be a really good and legitimate reason that he was on the scene. Detectives do not handle cases that they have any personal stake in. If the detective knows the people involved or is friends with the owner of the location where the murder occurred, he wouldn't be assigned the case.
So, if you want him to be assigned to the case, make certain that it's an accidental stumbling across of the offense while he's out and about. That he isn't overloaded with cases and can handle a new one. And that he has no connection at all to the people involved, the location, or any possible suspects.