  We study a spectral function for $\bar{D}_0^*$ $(0^+)$ meson in symmetric and
neutron-rich asymmetric nuclear matter from the viewpoint of the partial
restoration of chiral symmetry. Nuclear matter is constructed by a parity
doublet model with hidden local symmetry which can reproduce properties at
normal nuclear matter density as well as those in the vacuum. $\bar{D}$ mesons
are introduced by the chiral partner structure. Our results show that a mass of
$\bar{D}$ ($0^-$) meson increases while a mass of $\bar{D}_0^*$ meson decreases
at mean field level as we increase the baryon density, reflecting the partial
restoration of chiral symmetry. In the spectral function for $\bar{D}_0^*$
meson, we find a threshold enhancement is remarkably enhanced which indicates
this peak is an appropriate probe to observe the partial restoration of chiral
symmetry in nuclear matter. We also find a resonance of $\bar{D}_0^*$ meson
revives at higher density due to a narrowing of the phase space. In the
spectral function in neutron-rich asymmetric nuclear matter, we observe the
threshold enhancement in negatively-charged $\bar{D}_0^*$ meson channel stands
at higher energy and its height is more enhanced compared to neutral
$\bar{D}_0^*$ meson channel, due to the violation of isospin symmetry. On the
other hand, the resonance of negatively-charged $\bar{D}_0^*$ meson is slightly
suppressed compared to the neutral one.
