I was able to find some information on a person who died there in 1929. I was in Parsons last month and after seeing a list of burials at the hospital cemetery at findagrave.com (
http://www.findagrave.com/cgi-bin/fg.cgi?page=gsr&GScid=...), I had the name I was searching for and a death date. I contacted the medical records department and was told to provide a notarized letter requesting the information I wanted. They provided some details - name, date of birth, date of admission, date and cause of death. It was enough for me to request a death certificate from Kansas vital records though.
You can google for the number and address for Parsons State Hospital and Training Center (the name since 1957).
Good luck.
Joyce Coker