The Alabama state census of 1866 took place in conformity to an antebellum law requiring one to be taken every ten years. Civil disorganization in 1865 obliged authorities to conduct this one year late.

If I'm not mistaken, Reconstruction and radical rule didn't begin until 1867.

One interesting side note, Confederate civil and military records were preserved and organized so that Federal officials could prove allegiance of individual citizens in the Southern states.