The Collaborative International Dictionary of English v.0.48:

Tatta \Tat"ta\ (t[a^]t"t[.a]), n. [Hind. [.t]a[.t][.t][imac],
   t[=a]t[imac].]
   A bamboo frame or trellis hung at a door or window of a
   house, over which water is suffered to trickle, in order to
   moisten and cool the air as it enters. [India]
   [1913 Webster]