The ceiling in one of the archive rooms at the Torrox Court collapsed on Friday morning, covering files in water and sewage.
The collapse also damaged a server used to store recorded statements. No-one was injured in the incident.
There have reportedly been complaints about the state of the building, a 150-year-old structure which has never been adapted to modern needs. Judges needing to take statements from anyone with disabilities have to go down to the reception to perform the task as there are apparently no lifts in the building.