Actually, in the "misaligned, askew, etc." sense, I think that's the other way around. Crazy/crazed as a synonym for cracked (/flawed, damaged in that specific way) seems (according to the OED) to have come first, and been adopted metaphorically first for any infirmity (including sickness) and then for mental illness. All, mind you, within a relatively short period of time (within a half century to a century).

Its application in that strict sense survives in terms like "crazy-quilt" and as an adjective for a particular style of stone paving, or to a particular style of pottery glazing. (That is, "exhibiting the characteristics of random cracking".)

The etymology seems to be that "craze" (as a verb, from which comes "crazy") derives from Swedish through Norman French, from a verb "to dash to pieces", i.e. to shatter. From that you get "crazed" meaning something that gives the appearance of having been broken/cracked. It seems to have taken two centuries or more for the meaning to migrate in English to its application to "broken in body" or "broken in mind".

... Which is not to say I'm thus arguing that it's A-OK. As someone mentioned in a thread above, common usage trumps origins. But (I find) it's interesting to know.

I think at this point it's all-but impossible to divorce it from its "mental illness" meaning if you are applying it to a person. That is -- it seems possible, from the OED's entries, to think that describing someone's actions as "crazy" may in some cases derive not from "mentally ill" but from a comparison with jumpy and random nature of lines and shapes characteristic of the literal meaning (similar to "crazy quilt"). Possible. But also splitting hairs, since that won't be the first association to leap to anyone else's mind. Most people, upon hearing someone called crazy, will think, "oh, you mean cracked in the head", and other such synonyms for mental illness. So, yeah.