We report a measurement of time-integrated CP-violation asymmetries in the resonant substructure of the three-body decay D0→KS0π+π- using CDF II data corresponding to 6.0  fb-1 of integrated luminosity from Tevatron pp̅ collisions at √s=1.96  TeV. The charm mesons used in this analysis come from D*+(2010)→D0π+ and D*-(2010)→D̅ 0π-, where the production flavor of the charm meson is determined by the charge of the accompanying pion. We apply a Dalitz-amplitude analysis for the description of the dynamic decay structure and use two complementary approaches, namely, a full Dalitz-plot fit employing the isobar model for the contributing resonances and a model-independent bin-by-bin comparison of the D0 and D̅ 0 Dalitz plots. We find no CP-violation effects and measure an asymmetry of ACP=(-0.05±0.57(stat)±0.54(syst))% for the overall integrated CP-violation asymmetry, consistent with the standard model prediction.
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