If an exact $\mu \leftrightarrow \tau$ symmetry is the explanation of the maximal atmospheric neutrino mixing angle, it has interesting implications for the 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 is nonzero and is given directly by the solar mass difference square. We also find an upper bound on the lightest neutrino mass.

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