Where does bats in belfry come from?

The belfry being the uppermost room of a church, becomes analogous to the head in the same way that an unhinged or mentally defective person is described by 'the elevator doesn't go to the top floor'. The bat analogy for defective mental processes occurs in terminology like 'batty', 'moon bat', 'bat s**t crazy' and such. It probably derives from the unpredictable flight path of bats.