The modern meanings were beginning to come into the language in the early 1600s, but in Shakespeare we find only the earliest sense. This was essentially physical in character. Something that was crazy was full of cracks and flaws (as in modern crazy paving), damaged, or broken down.
Bodies as well as buildings could be crazy, therefore - as when Talbot says to Bedford: "We will bestow you in some better place, Fitter for sickness and for crazy age" (Henry VI Part 1, III.ii.89). Here the word means "frail" or "infirm". It is the only use of crazy in Shakespeare; but there is a related word, crazed, which is used by Demetrius to Lysander in A Midsummer Night's Dream (I.i.92): "yield Thy crazed title to my certain right". Here it means "flawed, unsound".
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin