When the U.S. Census began enumerating individuals by name in 1850, and asking a few health questions, the designations for idiocy and insanity began to crop up. The census enumerators were even given some definitions and instructions to distinguish the two. I encountered one case of this and found some references discussing the subject:
As far as I can tell, there was no backup medical diagnosis for use of those terms, and I suspect the census enumerators didn't attempt any verification, but just went by whatever they were told by the responding household member. I have seen the column checked on some U.S. census forms for people who appear to have lived normal lives. In a couple of cases, people seemed to be labeled only because they could not read or write.
There are a couple of links to the references that discuss this on the Buhrman-18 profile. They apply to the U.S. census, and I can't say whether there is any difference about the way this would have been handled in Arkansas, or any other state census.