沙汰 (sata: affair, state) sand + to sift out
This compound originally meant “to extract gold from sand,” as with panning for gold. A wide variety of meanings have accumulated, including these: “correspondence, verdict, conduct.”
In 狂気の沙汰 (kyōki no sata: crazy deed) and in the opposite phrase, 正気の沙汰 (shōki no sata: sane conduct, where 正気 breaks down as normal + spirit), 沙汰 means “conduct.”
In other cases, it does mean “correspondence.” For example, if someone has been out of touch with you for a long time, that person might start a letter with this expression:
長らくご無沙汰しています。
Nagaraku gobusata shite imasu.
I haven’t contacted you for a long time.長らく (nagaraku: (for a) long time)
ご無沙汰 (gobusata: lack of correspondence, being out of touch)
no + correspondence (last 2 chars.)