For mental patients the average length of stay in a psychiatric hospital or mental hospital is between 10 days to 30 days depending on how severe the mental health of the mental patient is.
Sometimes a mental health patient may only need to be held for 24 hours to 72 hours and sometimes due to a court order the mental health patient may need to be held much longer until they are no longer seen as a threat to themselves or the community.
If the patient needs held longer than 72 hours then they must get a court order to hold the patient longer than the 72 hours.
You also must be discharged from the mental hospital by mental hospital staff because you can't just walk out of the psychiatric hospital even if you admit yourself to the psychiatric hospital.