We search for CP nonconservation in the decays of tau leptons produced via
e(+)e(-) annihilation at roots similar to 10.6 GeV. The method uses correla
ted decays of pairs of tau leptons, each decaying to the pi pi (0)nu (tau)
final state. The search is done within the framework of a model with a scal
ar boson exchange. In an analysis of a data sample corresponding to 12.2 x
10(6) produced tau pairs collected with the CLEO detector, we find no evide
nce of violation of CP symmetry, We obtain a limit on the imaginary part of
the coupling constant parametrizing the relative contribution of diagrams
that would lead to CP violation to be -0.046<Im(<Lambda>)<0.022 at 90% C.L
This result provides a restriction on CP nonconservation in tau lepton deca
ys. As a cross-check, we study the decay angular distribution and perform a
model-independent search for a CP violation effect of a scalar exchange in
single <tau>--> pi (0)nu (tau) decays. The limit on the imaginary part of
the tau scalar coupling is -0.033 <Im(<Lambda>)<0.089 at 90% C.L.