1510s, "tangled or matted" (of hair), Scottish, probably related to Old English tættec "a rag" (see tatter (n.)). Sense of "tattered, ragged, shabby" first recorded 1933.
an old house with dirty windows and tatty curtains
tattersall
tatting
tattle
tattletale
tattoo
tatty
tau
taught
taunt
taupe
taurine