'Techt, a. informal. (alteration of touched, a word of the same meaning; c.f. obsolete tached, meaning "of a given disposition")
An alternative spelling is teched
Slightly crazy or mentally imbalanced.
One of my grandmother's favorite expressions was "Both thee and I's a bit tetched, but thee's a bit more tetched than I." Meaning: we're both a little crazy, but you're crazier than I am.
My grandmother came originally from the Appalachian mountains of Tennessee, where her family had lived since the close of the civil war. A curious linguistic anomaly of the area (especially the Ozarks) is that many grammatical forms found in the dialect of the region can be traced to 18th century Scottish English, though they have since fallen into disuse in the rest of the world. In particular, use of the obsolete pronouns thee and thy, the use of the word "till" to mean "because", and use of double modal auxiliary verbs ("might could"). The use of "you all" (or "y'all" as it's more frequently rendered) is also considered by some to be a replacement for the obsolete plural "ye."
By the time I was born, my mother had moved to California and my grandmother had resettled in a nearby coastal town. I grew up hearing this expression, and over time it became part of my own language. It wasn't until middle school that my friends and teachers began to question me as to the origin of my peculiar little catch phrase, and I realized how odd it sounds to a speaker of modern English.
Sources: personal experience, and http://220.127.116.11/sheproom/periodicals/ozarkswatch/ow803j.htm