There is no centralized government database of information about you, and the Census has no access to information from the IRS, etc (and likewise, other government agences have no access to information about individuals from the Census; the FBI has actually tried a couple times to get Census data, but they were shot down in court.)
There may be no “centralized” data base, but they already have the information in their memories, and you have to be nuts to thing that they aren’t indexing it.
This isn’t census data, it’s all of the things like house size, from the town permit data, residents, from school lists and voter registration, ect.
They don’t need to ask, as they already know. And with the advances in computing power, I’ve no doubt that most of it is already indexed.