You know immediately that everything you do will be splashed all over the daily tabloids, which means you have to drastically alter the way you planned to deal with the crime.
This is how I normally deal with a burglary:
Step One: Attend, look at broken window/door, nod and make encouragingly expert noises.
Step Two: Record details of what has been stolen.
Step Three: Explain to the victim that we will be doing house-to-house enquiries, local intelligence checks, CCTV, and identifying people from line-ups.
Step Four: Do no further work, but hand over the whole investigation to Scenes of Crime.
Unfortunately your average Celebrity Burglary is likely to require all of those actions and more, as there is also a high chance that the burglary was done by a Stalker. This combines a crime which is impossible to investigate with a crazed lunatic and intense press coverage.
I think I'll just say I'm stuck in the office doing paperwork when that one comes in.