The 1900 Wayne County "Insane Asylum" was known as The Wayne County House and Insane Asylum. Although the census contains both the "Insane" and ill and the County Poor, they are separated by a blank page on the census sheets.
The Census Taker is listed as W.B. James M.D., and he started the documentation June 1, 1900. Enumeration District 212 Township: Nankin Pg 326A. He also attempted to keep the patients in alphabetical order, there are several mistakes, so you need to be careful when searching.
Below are the extracted "insane" or chronically ill patients, listed and spelled as I found them in the census, keeping in mind sometimes its hard to read someone else's handwritting, I attempted to transcribe them as best I could, and this is partial data, for full information, refer to the census itself. (There are also patients, Herbetz, Arthur age 11 yrs and Miller, John age 14 yrs ; I'm not quite sure how got listed or admitted in here with the adults)