  If an exact $\mu\leftrightarrow \tau$ symmetry is the explanation of the
maximal atmospheric neutrino mixing angle, it has interesting implications for
origin of matter via leptogenesis in models where small neutrino masses arise
via the seesaw mechanism. For seesaw models with two right handed neutrinos
$(N_\mu, N_\tau)$, lepton asymmetry vanishes in the exact $\mu\leftrightarrow
\tau$ symmetric limit, even though there are nonvanishing Majorana phases in
the neutrino mixing matrix. On the other hand, for three right handed neutrino
models, lepton asymmetry nonzero and is given directly by the solar mass
difference square. We also find an upper bound on the lightest neutrino mass.
