  We study the effect of a light charged Higgs appearing in supersymmetric
models containing two Higgs doublets on the measurement of leptonic branching
ratios of the W boson at LEP. We show that the $2.8 \sigma$ excess of the
branching ratio $W \to \tau \nu$ with respect to the other leptons correlates
well with the existence of charged Higgs with mass close to the mass of the W
boson which dominantly decays into $W^\star$ and a light CP odd Higgs boson $A$
with mass below $2m_b$, so that it decays into $\tau^+ \tau^-$ and $c \bar c$.
There are no searches for the charged Higgs in this channel and thus it could
be discovered in LEP data or at the Tevatron where it would be frequently
produced in top quark decays.
