Just to follow up:

According to a number of sources I've studied, the census returns (tabulae censoriae) would be stored at the specialised archive located in the Temple of The Nymphs in Rome.

Here is what Wikipedia has regarding that Temple's fate:

The temple was founded in the 3rd century BC or the early 2nd century BC. It was damaged by a fire in the mid 1st century BC and probably also affected by the citywide fire in 80 AD. This temple was on the Campus Martius. If still in use by the 4th-century, the temple would have been closed during the persecution of pagans in the late Roman Empire, when the Christian Emperors issued edicts prohibiting all non-Christian worship and sanctuaries.

So the temple was closed, but what happened to the priceless archive that was located there remains unclear.

Amen.

Thanks for your post, cb.