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 $772 times 10^6$ $Boverline{B}$ 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 $m_{h} simeq m_{B^0} pm 3~mathrm{GeV}/c^2$.
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