The Collaborative International Dictionary of English v.0.48:

Batty \Bat"ty\ (b[a^]t"t[y^]), a.
   1. Belonging to, or resembling, a bat. "Batty wings." --Shak.
      [1913 Webster]

   2. Crazy; demented; loony; nuts; as, her constant gabbing is
      driving me batty. [Colloq.]

   Syn: bats.
        [PJC]

WordNet (r) 3.0 (2006):

batty
    adj 1: informal or slang terms for mentally irregular; "it used
           to drive my husband balmy" [syn: balmy, barmy,
           bats, batty, bonkers, buggy, cracked,
           crackers, daft, dotty, fruity, haywire,
           kooky, kookie, loco, loony, loopy, nuts,
           nutty, round the bend, around the bend, wacky,
           whacky]

Moby Thesaurus II by Grady Ward, 1.0:

82 Moby Thesaurus words for "batty":
   apish, asinine, balmy, bananas, barmy, bats, beany, bedlamite,
   befooled, beguiled, besotted, bonkers, brainless, buffoonish,
   buggy, bughouse, bugs, cockeyed, cracked, crackers, crazed, crazy,
   credulous, cuckoo, daffy, daft, dazed, deranged, dippy, dizzy,
   doting, dotty, dumb, fatuitous, flipped, fond, fool, foolheaded,
   foolish, freaked-out, fruitcakey, fruity, fuddled, futile, gaga,
   goofy, gulled, haywire, idiotic, imbecile, inane, inept,
   infatuated, insane, just plain nuts, kooky, loony, loopy, mad,
   maniac, maudlin, moronic, nuts, nutty, off the hinges,
   off the track, off the wall, potty, round the bend, sappy,
   screwball, screwballs, screwy, senseless, sentimental, silly,
   slaphappy, stupid, thoughtless, wacky, wet, witless