$b\to s\gamma$ and $Z\to b\bar{b}$ Constraints on Two Higgs Doublet Model

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 $Z\to b\bar{b}$ 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 $\tan \beta <1$.