  We present a search for the dark photon $A^{\prime}$ in the $B^0 \to
A^{\prime} A^{\prime}$ decays, where $A^{\prime}$ subsequently decays to $e^+
e^-$, $\mu^+ \mu^-$, and $\pi^+ \pi^-$. The search is performed by analyzing
$772 \times 10^6$ $B\overline{B}$ events collected by the Belle detector at the
KEKB $e^+ e^-$ energy-asymmetric collider at the $\Upsilon (4S)$ resonance. No
signal is found in the dark photon mass range $0.01~\mathrm{GeV}/c^2 \le
m_{A^{\prime}} \le 2.62~\mathrm{GeV}/c^2$, and we set upper limits of the
branching fraction of $B^0 \to A^{\prime} A^{\prime}$ at the 90\% confidence
level. The products of branching fractions, $\mathcal{B}(B^0 \to A^{\prime}
A^{\prime}) \times \mathcal{B}(A^{\prime} \to e^+ e^-)^2$ and $\mathcal{B}(B^0
\to A^{\prime} A^{\prime}) \times \mathcal{B}(A^{\prime} \to \mu^+ \mu^-)^2$,
have limits of the order of $10^{-8}$ depending on the $A^{\prime}$ mass.
Furthermore, considering $A^{\prime}$ decay rate to each pair of charged
particles, the upper limits of $\mathcal{B}(B^0 \to A^{\prime} A^{\prime})$ are
of the order of $10^{-8}$-$10^{-5}$. From the upper limits of $\mathcal{B}(B^0
\to A^{\prime} A^{\prime})$, we obtain the Higgs portal coupling for each
assumed dark photon and dark Higgs mass. The Higgs portal couplings are of the
order of $10^{-2}$-$10^{-1}$ at $m_{h'} \simeq m_{B^0} \pm 40~\mathrm{MeV}/c^2$
and $10^{-1}$-$1$ at $m_{h'} \simeq m_{B^0} \pm 3~\mathrm{GeV}/c^2$.
