If you go to check yourself into a mental hospital voluntarily then no you cannot just check yourself out of the mental hospital when you decide you want to leave.
You must stay for the 48 hours to 72 hours or the time frame they are allowed to legally hold you.
Then if they deem you are a threat to yourself or to society then the mental hospital can get a court order to hold you involuntarily which means that you then become an involuntary mental patient.
Also if someone commits you to a mental hospital then you cannot check yourself out then either and must be held until the mental hospital lets you go legally.
So either way you must be discharged from the mental hospital by the mental hospital staff before you are allowed ot leave the mental hospital.