  We study the lepton electric dipole moments in the framework of the
supersymmetric type II seesaw model where the exchange of heavy SU(2)_W
triplets generates small neutrino masses. We show that the CP violating phase
of the bilinear soft supersymmetry breaking term associated with the SU(2)_W
triplets contributes to lepton electric dipole moments mainly through threshold
corrections to the gaugino masses at the seesaw scale. As a consequence, the
ratio of the electric dipole moments of the muon and the electron is the same
as the ratio of their masses in a wide region of parameter space.
