  We perform a combined analysis of two stringent constraints on two Higgs
doublet model, coming from the recently announced CLEO II bound on $B(b
\rightarrow s \gamma)$ and $Z \rightarrow b \overline b$ and from the recent
LEP data on the ratio $\Gamma(Z\rightarrow b\overline
b)\over{\Gamma(Z\rightarrow hadrons)}$. We include one-loop vertex corrections
to $Z \rightarrow b \overline b$ in the model. We find that although the CLEO
II bound serves as the strongest constraint present in the charged Higgs sector
of the model, the current LEP value for $R_b$ may also provide a further
constraint for $\tan\beta<1$.
