Apologies for not taking time out of my day to write a full and formal experimental design.
If I were investigating the book-shelf incident, the first thing I'd want to verify was that the homeowners weren't making it up or faking it to wind each other up, or they have a child doing it, or rats, or whatever. Hence, a bunch of cameras.
(I picked HD cameras, because so many 'ghosts' seem to be recorded in low res with poor lighting despite the current high saturation of mains electricity and HD cameras. Odd that.)
You'd then want to start ruling out obvious things like vibrations from local roads or trainlines. Again, the cameras would give timings which might synch with the local train line, or blasting times at the local quarry, or when the delivery arrives at the local supermarket, or whatever.
From the film footage, you can calculate velocities and trajectories, and therefore energies and from there you could devise more specific tests. Obviously, you'd also check that the shelves were level and fitted properly.
To say much more from the description of "some books fell off some shelves and it was spooky" is pretty difficult really. You'd want to rule out obvious natural causes before you want any further and checked whether the structure of this roof cap is exactly like the kind of telemetry tracker that NASA uses to identify dead pulsars in deep space using cold riveted girders with cores of pure selenium.