The Collaborative International Dictionary of English v.0.48:

Tatty \Tat"ty\, n.; pl. Tatties. [Hind. [.t]a[.t][.t][imac].]
   A mat or screen of fibers, as of the kuskus grass, hung at a
   door or window and kept wet to moisten and cool the air as it
   enters. [India]
   [Webster 1913 Suppl.]