  In this paper, we study the extended Standard Model (SM) with an extra Higgs
doublet and right-handed neutrinos. If the symmetry to distinguish the two
Higgs doublets is not assigned, flavor changing neutral currents (FCNCs)
involving the scalars are predicted even at the tree level. We investigate the
constraints on the FCNCs at the one-loop level, and especially study the
semileptonic $B$ meson decays, e.g. $B \to D^{(*)} \tau \nu$ and $B \to K^{(*)}
ll$ processes, where the SM predictions are more than $2 \sigma$ away from the
experimental results. We also consider the flavor-violating couplings involving
right-handed neutrinos and discuss if the parameters to explain the excesses of
the semileptonic $B$ decays can resolve the discrepancy in the the anomalous
muon magnetic moment. Based on the analysis, we propose the smoking-gun signals
of our model at the LHC.
