All your data? No, just records of whether or not your a citizen/resident. That seems like pretty important data for any government to have. It's also information the state's records department likely already has. For example, if you have a drivers license with the state or you were born in the state they'll have that documentation.

Unless you are just an anarchist, then I can't see how it's unreasonable for a government to know who it represents. That's why governments do censuses. Heck, that's needed just for the basic function of making sure you aren't voting in multiple districts.