  We calculate the new physics contributions to the neutral $B_d^0$ and $B_s^0$
meson mass splitting $\Delta M_d$ and $\Delta M_s$ induced by the box diagrams
involving the charged-Higgs bosons in the top quark two-Higgs doublet model
(T2HDM). Using the precision data, we obtain the bounds on the parameter space
of the T2HDM: (a) for fixed $M_H=400$ GeV and $\delta=[0^\circ,60^\circ]$, the
upper bound on $\tan{\beta}$ is $\tan \beta \leq 30$ after the inclusion of
major theoretical uncertainties; (b) for the case of $\tan{\beta} \leq 20$, a
light charged Higgs boson with a mass around 300 GeV is allowed; and (c) the
bounds on $\tan{\beta}$ and $M_H$ are strongly correlated: a smaller (larger)
$\tan{\beta}$ means a lighter (heavier) charged Higgs boson.
