1510s, "tangled or matted" (of hair), Scottish, probably related to Old English tættec "a rag" (see tatter (n.)). The sense of "tattered, ragged, shabby" attested by 1933.
Entries linking to tatty
tatter n.
c. 1400, tatrys (plural) "slashed garments," from a Scandinavian source such as Old Norse töturr "rags, tatters, tattered garment," cognate with Old English tættec, tætteca "rag, tatter." Related: Tatters.