  We report the first observation of the $\psi(4415)$ resonance in the reaction
$\e^+e^-\to D^0 D^-\pi^+$ and a measurement of its cross section in the
center-of-mass energy range $4.0\mathrm{GeV}$ to $5.0\mathrm{GeV}$ with initial
state radiation. From a study of resonant structure in $\psi(4415)$ decay we
conclude that the $\psi(4415)\to D^0 D^-\pi^+$ decay is dominated by
$\psi(4415)\to D \bar D{}^{*}_2(2460)$. We obtain $\mathcal{B}(\psi(4415)\to
D^0 D^-\pi^+_{\mathrm {non-resonant}})/\mathcal{B}(\psi(4415)\to D \bar
D{}^{*}_2(2460)\to D^0 D^-\pi^+)<0.22$ at 90% C.L. The analysis is based on a
data sample collected with the Belle detector with an integrated luminosity of
673 $\mathrm{fb}^{-1}$.
