Search for CP Violation in D⁰--> K_S⁰ pi^+pi^-

We report on a search for CP violation in the decay of D0 and D0B to Kshort pi+pi-. The data come from an integrated luminosity of 9.0 1/fb of e+e- collisions at sqrt(s) ~ 10 GeV recorded with the CLEO II.V detector. The resonance substructure of this decay is well described by ten quasi-two-body decay channels (K*-pi+, K*0(1430)-pi+, K*2(1430)-pi+, K*(1680)-pi+, Kshort rho, Kshort omega, Kshort f0(980), Kshort f2(1270), Kshort f0(1370), and the ``wrong sign'' K*+ pi-) plus a small non-resonant component. We observe no evidence for CP violation in the amplitudes and phases that describe the decay D0 to K_S^0 pi+pi-.