  We prove a conjectural formula relating the Bessel period of certain
automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is
proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the
groups $(\SO(5), \SO(2))$. The conjecture has been previously proved for
certain automorphic forms on $\mathrm{GSp_4}$ from lifts. In this paper, we
extend the formula to Siegel modular forms of $\Sp_4(\bZ)$.
