The phrase BATS IN THE BELFRY means crazy or eccentric.
The phrase has the sound of a phrase from Olde Englande and it certainly has the imagery to fit into any number of Gothic novels based in English parsonages or turreted castles. In fact, it comes from the USA and is not especially old. This article from the Ohio newspaper The Newark Daily Advocate, October 1900 includes it:
“To his hundreds of friends and acquaintances in Newark, these purile [sic] and senseless attacks on Hon. John W. Cassingham are akin to the vaporings of the fellow with a large flock of bats in his belfry.”