The Collaborative International Dictionary of English v.0.48:

Dotty \Dot"ty\, a. [From 2d Dot.]
   1. Composed of, or characterized by, dots.
      [Webster 1913 Suppl.]

   2. [Perh. a different word; cf. Totty.] Unsteady in gait;
      hence, feeble; half-witted. [Eng.]
      [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

dotty
    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]
    2: intensely enthusiastic about or preoccupied with; "crazy
       about cars and racing"; "he is potty about her" [syn:
       crazy, wild, dotty, gaga]