  $CP$ violation and branching fraction measurements in $D$ decays are
interesting topics as any difference with respect to the Standard Model
prediction would be an indication of new physics. With the large data sample
collected by the Belle detector, which sits at the interaction point of KEKB
asymmetric $e^{+} e^{-}$ collider in Japan, we present the results of searches
for $CP$ violation in $D^{0}\rightarrow V\gamma~(V = \phi, \overline{K}^{*0},
\rho^{0})$ decay and the rare $D$ decay $D^{0}\rightarrow \gamma \gamma$.
