With no New Physics seen at the LHC, a second Higgs doublet remains attractive and plausible. The ratio $R_B^{\mu /\tau }=B(B\to \mu \overline{\nu })/B(B\to \tau \overline{\nu })$ is predicted at 0.0045 in both the Standard Model and the two Higgs doublet model type II, but it can differ if extra Yukawa couplings exist in Nature. Considering recent Belle update on $B\to \mu \overline{\nu }$, the ratio could be up by a factor of two in the general two Higgs doublet model, which can be probed by the Belle II experiment with just a few ab$^{−1}$.