Continuity mistake: During episode 6-3, it is established that all inmates at the Ohio prison facility are required to have their hair cut in order to prevent the spreading of lice. Later on in the series, it is revealed that almost all of the inmates that were not moved to Litchfield Max after the riot were sent to Ohio. Despite that, several of the inmates formerly from Litchfield were shown still having long hair in scenes that took place in the Ohio facility, and Maritza's hair was long when she first appeared at the nightclub while she was on parole. While it is possible that the policy may have been rescinded between the events of seasons six and seven (which would explain why Alex's hair was still long when Piper visited her), that does not explain the other characters that were immediately transferred to Ohio still having their hair long during subsequent appearances.
Plot hole: "Red" is somehow serving a life term or what for the execution murders of some Russian spies, her husband and his cronies had headed up. But her hubby somehow escaped any such sentencing.
Answer: You would need to be more specific as to which inmate to get an answer as to who possibly belongs in the mental ward. In general; usually the only mentally ill prisoners who go to the mental ward are inmates who show obvious psychotic breaks like Loli and crazy eyes as, with the conditions of prison, it's often difficult to tell who is mentally ill and whose frustrated from the conditions. Many of them are also only there temporarily. Crazy Eyes, first example, was in the mental ward. Her mother fought and won to get her out.