  We report on a theoretical study of the $\pi^- p \to D^- D^0 p$ reaction near
threshold within an effective Lagrangian approach. The production process is
described by $t$ channel $D^{*0}$ meson exchange, $s$-channel nucleon pole, and
$u$ channel $\Sigma^{++}_{c}$ exchange. In our work, the final $D^0 p$ results
from the ground $\Lambda^+_c(2286)$ state and also dominantly from the excited
$\Lambda^+_c(2940)$ state which is assumed as a $D^{*0} p$ molecular state with
spin parity $J^P = \frac{1}{2}^+$ or $\frac{1}{2}^-$. We calculate the total
cross section of the $\pi^- p \to D^- D^0 p$ reaction. It is shown that the
spin parity assignment of $\frac{1}{2}^-$ for $\Lambda^+_c(2940)$ gives a
sizable enhancement for the total cross section in comparison with a choice of
$J^p = \frac{1}{2}^+$. However, our theoretical result of the total cross
section is sensitive to the value of the cutoff parameter involved in the form
factor of the exchanged off-shell particles. Moreover, we also calculate the
second order differential cross section and find it can be used to determine
the parity of the $\Lambda^+_c(2940)$. It is expected that our model
calculations can be tested by future experiments at J-PARC in Japan.
