Fig.: to be eccentric or a little bit crazy

When Martin said he was saving to buy a space-ticket to Mars, he was thought to have bats in his belfry

Quando Martino ha detto di voler risparmiare per comperarsi un biglietto spaziale per Marte, tutti hanno pensato che fosse un povero picchiatello

When I told her that I like walking very early in the morning through marshes looking for insects, she looked at me as I had bats in my belfry

Quando le ho detto che amo andare il mattino presto per paludi in cerca di insetti, mi ha guardato come se fossi un po' tocco

This American expression was coined in the late 1800s and made popular in the early 1900s. It seems it became popular as much through its alliteration as through any great appropriateness: it refers to the way bats that live in a belfry (the part of a church tower where bells are hung) fly frantically from it when the bells are rung. In such an analogy the belfry represents the head and bats the wild and disordered thoughts of a disturbed mind