We have performed the first search for CP violation in tau lepton deca
y. CP violation in lepton decay does not occur in the minimal standard
model but can occur in extensions such as the multi-Higgs doublet mod
el. It appears as a characteristic difference between the tau(-) and t
au(+) decay angular distributions for the semileptonic decay modes suc
h as tau(-) --> K-0 pi(-) nu. We define an observable asymmetry to exp
loit this and find no evidence for any CP violation. [S0031-9007(98)07
548-6].