  We study a $\mu - \tau$ reflection symmetry in neutrino sector realized at
the GUT scale in the context of the seesaw model. In our scenario, the exact
$\mu - \tau$ reflection symmetry realized in the basis where the charged lepton
and heavy Majorana mass matrices are diagonal, leads to vanishing lepton
asymmetries. We find that, in the minimal supersymmetry extension of the seesaw
model with appropriate values of $\tan\beta$, the renormalization group (RG)
evolution from the GUT scale to seesaw scale can induce a successful
leptogenesis. It is shown that the right amount of the baryon asymmetries
$\eta_B$ can be achieved via so-called resonant leptogenesis, which can be
realized at rather low seesaw scale in our scenario, so that the well-known
gravitino problem is safely avoided. In this work, we consider both flavor
dependent and flavor independent leptogenesis, and demonstrate how they lead to
different amounts of baryon asymmetries in detail.
