It has been known that R b can be enhanced in the two Higgs doublet model if tan β is large. We point out that a similar enhancement in Γ(Z → τ + τ - ) is large enough to place a constraint on such a possibility. We obtain a 95% CL upper bound ΔR b /R b < 0.73% in this model for the MS massm b (m Z ) = 3.0 GeV. The 1996 world average is ΔR b /R b = 0.97% ± 0.51%. We used the m b (m Z ) to determine the bottom Yukawa coupling instead ofm b (m b ) unlike in previous analyses, and also an improved experimental test of the lepton universality in Z decay, which made our results qualitatively different.