  We investigate the in-medium masses of a $\bar{D} (0^-)$ meson and a
$\bar{D}_0^* (0^+)$ meson and spectral functions for $\bar{D}$ and
$\bar{D}_0^*$ meson channels in nuclear matter. These mesons are introduced as
chiral partner in the chiral symmetry broken vacuum, hence they are useful to
explore the partial restoration of the broken chiral symmetry in nuclear
matter. We consider the linear sigma model to describe the chiral symmetry
breaking. Our study shows that the loop corrections to $\bar{D}$ and
$\bar{D}_0^*$ meson masses provide a smaller mass splitting at finite density
than that in vacuum, whose result indicates a tendency of the restoration of
the chiral symmetry. We investigate also the spectral function for
$\bar{D}_0^*$ meson channel, and find three peaks. The first peak which
corresponds to the resonance of $\bar{D}_0^*$ meson is broadened by collisions
with nucleons in medium, and the peak position shifts to lower mass due to the
partial restoration of chiral symmetry as the density increases. The second
peak is identified as a threshold enhancement which shows a remarkable
enhancement as the density increase. The third peak is Landau damping. The
obtained properties of $\bar{D}$ and $\bar{D}_0^*$ mesons in nuclear matter
will provide useful information for experiments.
