Search for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>violation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>S</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

We report on a search for $CP$ violation in the decay of ${D}^{0}$ and ${\overline{D}}^{0}$ to ${K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. The data come from an integrated luminosity of $9.0\text{ }{\mathrm{f}\mathrm{b}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ collisions at $\sqrt{s}\ensuremath{\approx}10\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}$ recorded with the CLEO II.V detector. The resonance substructure of this decay is well described by ten quasi-two-body decay channels plus a small nonresonant component. We observe no evidence for $CP$ violation in the amplitudes that describe the decay ${D}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$.