These comments generally apply to US research on those individuals who were sent to a state “asylum” for the “insane.” Keep in mind that the general meaning of that last word has changed over time.
Access to state hospital records is normally set by state statute–so if a court order is required, it’s required and the process in one state may be different that the process in another state.
Records of the committal are typically county court records and those may be open–you just need to find out what court handles those sorts of cases during the time period in question. In some areas, they may be town records.
There may also be references to the case in the newspaper–not as likely, but possible depending upon the situation. Of course those records would be public.
For the first two instances, I’d reach out to a statewide genealogy group–there should be some on Facebook. Someone there could give you pointers for the state of interest as state statute and the court structure would determine access and the process for getting at state hospital records. Local court records may be open–again depending upon the state. Get both sets of records. While some information may be duplicated some details will be unique to the record.
Newspapers (assuming they are online somewhere) should not be a big problem. But you may have to access them on microfilm and in that case, without a date, a search will take time. I would wait searching non-digitized newspapers until you have a date or time period of the committal.