I don't know any stats it would be interesting to find.
I attempted suicide as a JW while at bethel but before becoming a JW I had attempted suicide due to circumstances at non JW home.
I don't know about Patterson or Walkill but Brooklyn has a room set up like a psych unit and there is a psychologist on staff. I heard there is another one after I left but I can't verify that. I use to clean the pharmacy at bethel and what finally helped me get over shame about using meds if I needed to was seeing lithium and anti-depressants on the shelf.
I know # of people with mental health issues they've all said they had these problems before becoming a JW. Being one has not helped them since therapy is looked down on. I did my best to encourage those who needed help to get it.
Commenting on Haggai 2:7 “‘And I will rock all the nations, and the desirable things of all the nations must come in; and I will fill this house with glory,’ Jehovah of armies has said"; my husband said how loving that Jehovah calls all in the organization who suffer from mental illness desirable. At the time I agreed now it makes me sad that those who truly need help are taken advantage of.