  The time-integrated Dalitz plot of the three-body hadronic charmless decay
${{\overline{B}}^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^+ \pi^-}$ is
studied using a $pp$ collision data sample recorded with the LHCb detector,
corresponding to an integrated luminosity of $3.0\;\mathrm{fb}^{-1}$. The decay
amplitude is described with an isobar model. Relative contributions of the
isobar amplitudes to the ${\overline{B}^0 \to K_{\mathrm{\scriptscriptstyle
S}}^0 \pi^+ \pi^-}$ decay branching fraction and CP asymmetries of the
flavour-specific amplitudes are measured. The CP asymmetry between the
conjugate ${\overline{B}^0 \to K^{*}(892)^{-}\pi^+}$ and ${\overline{B}^0 \to
K^{*}(892)^{+}\pi^-}$ decay rates is determined to be $-0.308 \pm 0.062$.
