  The first study is presented of CP violation with an amplitude analysis of
the Dalitz plot of $B^0 \to D K^+ \pi^-$ decays, with $D \to K^+ \pi^-$, $K^+
K^-$ and $\pi^+ \pi^-$. The analysis is based on a data sample corresponding to
$3.0\,{\rm fb}^{-1}$ of $pp$ collisions collected with the LHCb detector. No
significant CP violation effect is seen, and constraints are placed on the
angle $\gamma$ of the unitarity triangle formed from elements of the
Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated
with the $B^0 \to D K^*(892)^0$ decay are determined for the first time. These
measurements can be used to improve the sensitivity to $\gamma$ of existing and
future studies of the $B^0 \to D K^*(892)^0$ decay.
