I do not live in MO, therefore thought it would be almost impossible to get any sort of information. I did finally make contact with the old hospitals present facility. A couple old buildings, I believe, still remain. I had to obtain "a court order" from a local judge and prove beyond any doubt that "all persons were now dead". I sent various documents including death certificates, obits, etc. My request was finally approved (I did NOT have to appear), then my approval was forwarded on to the present facility. I paid "a fee" (for photocopies, etc) and after about 3 months, what documents that were available for my great aunt, were mailed to me. I have not yet attempted to ask for info on my great grandmother. She died of TB at State Hospital #3 and is buried in the hospital cemetery. My great aunt's body was returned to Webb City.
I didn't get much, just a few pages, perhaps 8 at the most, but enough to give me the answers I needed.
I hope this helps. I will tell you though that not all records still exist. Some, I was told, were "put in storage". Many were put on microfilm. Those are the ones I received (i.e. copies) and not all that clear but good enough. I was happy with what I received.