If you type this into google you get one useful link.
bat-shit crazy, a. (often abbreviated to bat-shit)
Of persons : Not of sound mind, mad, insane, deranged, lunatic. Also to describe any state of frenzied rage, violence, excitement or intoxication. No longer in formal medical use.
Of ideas : To describe any bizarre, unfounded, heretical or otherwise objectionable belief or proposition.
For usage see e.g. 1390 Gower Conf. I. 46 For certes such a maladie, It myghte make a wisman batt shitte. 1507 Shakes Hamlet II.ii Pol : Mad call I it; for, to define true madness, what is't but to be bat-shit? 1910 S. Freud in Amer. Jrnl. Psychol. XXI. 193, I called this hypothetical state Fledermäuse-Scheiße (‘bat-shit’) and considered it was proved by the undeniable existence of resistance.
Of unknown derivation. Possibly :
1) A corruption of the term "batty", see also "bats in the belfry".
2) Relating to the hallucinatory effects of smoking the dried faeces of the Smoking Bat Amorphochilus schnablii.
To me those usages look a little suspect, and although I have heard it said by people who were doctors, or at least knew doctors, I don't think it has ever been in formal medical use - but it's a nice thought.
I have been thinking about this literally all day - where does the phrase come from? And all I can find is this teenage website of waffle. So disheartening. The reason I have been thinking about it though will soon become apparent.
Every professional body, membership organisation, group, congregation, gathering, collection etc of people has a certain percentage who are crazy. I'm not talking medically - I just mean they are so off the scale they think world peace just needs everyone to do what they say and eat acorns or something equally weird. They think the world is against them because they have brown eyes, not because they don't wash and abuse anyone who doesn't immediately agree with their impractical ideas. They go on about their ideas at length, get obsessed about trivialities of how the organisation is run and inevitably end up going off in a dramatic strop and trying to start a rival org with the other crazies. These people are a very small minority but account for a large proportion of the administrative work of the orgs because if you work for an org like that you can't just say "go away crazy" - you have to try and be rational and polite with them. If I were forced to make up a totally random figure based on personal experience of working with or for three such organisations I would say about 0.1%. That's 1 in a thousand for those non-knitters reading this. But the important thing is that every body has them and when they go crazy in the modern age, they do it online.
Picture a traditional organisation representing a proud profession. It has offices in central london which include a business centre - really an airy room with some nice chairs, a sofa and wifi with carefully chosen professional magazines on the sturdy, modern yet traditional coffee table. Now picture a crazy going into this place, because they are a member and therefore you can't stop them unless they start stealing the sugar sachets again, and meeting another crazy. Now imagine the second one (who's only role in life is to prove that there really is someone for everyone) "romances" the first in this business centre. Now imagine that the first writes about it on her website (crazy is equal opps) and describes the expensive leather modern yet traditional, sturdy sofa as "eminently suitable for the purpose". Then imagine she hacks into the website of the commercial arm of that body and turns it into a leacherous dating site, but giving the contact details and address of that organisation.
Now that is bat shit crazy. It's also quite funny for others working for similar organisations in the same way people reportedly laugh with relief when someone next to them gets killed but they survive unscathed.
Crazies, there is no doubt, cause a great deal of work and often misery for staff at these kind of organisations. I suspect they think they are doing it for the best - but possibly in the same way as the inquisition torturers did. While occasionally crazies can act as good team building material (whatever the differences between finance and sales you can all agree when someone is BSC and join to speculate as to their motives and personal habits) coming under fire from one does not make up for it in the long run. Sadly the crazies at the org I work for aren't as amusing as the romanced one in the example above - quite possibly because we are trying to close our equalivalent of a business centre due to financial cuts. Perhaps if we got the crazies together and let them romance each other they would be happier? Or at least stop sending me emails.