There seems to be a lot of confusion about how to get or ask for hospital records under governance by the Michigan Department of Community Health.
First, you must ask for the court order to view the records from the judge in the county that the Asylum was located. Not the county your family was living in; although, sometimes they are the same county. You call the court and ask for the name of the judge who authorizes medical record releases and then write that Judge, addressing him/her properly, for a court order for the medical records of so and so at the __________ Asylum/State Hospital. Your letter should be respectful and polite and should include your relationship to the patient, when they died, and why you feel that the records would help you (ie. to complete your family medical history). You should have a pretty good idea of when the person was there. If you are denied a court order and are willing to fight over this, then you can call back and argue with them that you will go through the process if need be to gain access to these records.
Second, the person was committed in the county in which they resided at the time and this generated probate court records. So these records fall within the county the person lived in, and this may not be the same county the asylum was in. Some counties have allowed these records to be digitized and available and you should exhaustively search the internet (including familysearch.org) for these records before you call or bother a court. I advise finding these records first as they will tell you when the person was sent to the asylum and why.
Third, if you live in state you can call your state rep or senator to assist you, and you can complain that these records are kept under lock and key but other records with private and personal data are available to anyone- such as the 1940 census. You can emphasize the importance of having these records to complete your family medical history as mental illness has an hereditary component.
Fourth, if you live out of state, you can call the state rep or senator for the district in which the Asylum was located and explain your difficulty in getting your family’s medical records for this asylum. The records are all in the State of Michigan Archives in Lansing and are under threat of destruction.
Good luck. You will need to be persistent and the records may not even tell you much.