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 correlated 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 scalar 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 evidence 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)<0.022 at 90% C.L This result provides a restriction on CP nonconservation in tau lepton decays. 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 --> pi (0)nu (tau) decays. The limit on the imaginary part of the tau scalar coupling is -0.033 )<0.089 at 90% C.L.
