It was brought up again so I thought I should make it an official hc so to make everyone aware in case there's any confusion. I like to be as realistic as possible when writing so, where Arkham is concerned, I write it how it is in life: genders are kept separate in Arkham, as it is not just an asylum... it is an asylum for the criminally insane. The distinction matters between the two - an inmate would first have to be convicted of a serious crime and then be declared insane or unfit for prison in order to be sent to Arkham; they are interned there until they are found to be fit to serve their actual sentence in a prison. Normal prison rules apply at Arkham. The only reason J has managed to constantly be sent there (other than having a mental disorder & a crooked lawyer) is due to the fact that Gotham has no death penalty, otherwise he would be long dead. I think this alone is mentioned in a comic or maybe I dreamt it.
I believe some residential clinics for mental health patients may not have a strict separation rule but in a place such as Arkham, the rule is there for a reason (I mean... do I need to elaborate here & mention how many predators/killers whom prey exclusively on women would probably be there? That is life, unfortunately).
This is how I choose to write within my Arkham verse & how I choose to paint the background of J's personal record. If this doesn't suit you, I'm sorry but I hope it doesn't discourage anyone!