1930, U.S. colloquial variant of touched in the sense of "slightly crazy" (see touch (v.)).
Entries linking to tetched
late 13c., "make deliberate physical contact with," from Old French tochier "to touch, hit, knock; mention, deal with" (11c., Modern French toucher), from Vulgar Latin *toccare "to knock, strike" as a bell (source also of Spanish tocar, Italian toccare), perhaps of imitative origin. Related: Touched; touching.
From c. 1300 in the transitive sense "bring into physical contact," also "pertain to." Other senses attested from 14c. are "perceive by physical contact, examine by sense of touch," also "be or come into physical contact with; come to rest on; border on, be contiguous with;" also "use the sense of touch," and "mention, describe." From early 14c. as "affect or move mentally or emotionally," with notion of to "touch" the heart or mind. Also from early 14c. as "have sexual contact with." Meaning "to get or borrow money" first recorded 1760.
Touch-and-go (adj.) is recorded from 1812, apparently from the name of a tag-like game, first recorded 1650s (however, despite the coincidence, this in no way suggests an acronym origin for tag). Touch football is first attested 1933. Touch-me-not (1590s) translates Latin noli-me-tangere.