As others have said the facility you should probably check is Dorothea Dix in Wake County (Raleigh). It used to be referred to as simply "State Hospital," or "State Hospital for the Insane."

The hospital still exists today but is no longer Dorothea Dix.

I was wondering if you have had any luck finding records? I have an ancestor who was listed there in the 1920 Wake County Census. I was able to find his death certificate but would like to find out why/how long he was there.

I have heard that there are records on file at the NC State Archives but have also heard that personal files are destroyed 10 years after death - so I'm not sure.

Hope you had luck finding information!