  A non-universal anomaly free $U(1)_{X}$ extension to the Minimal
Supersymmetric Standard Model, consisting of four scalar doublets, four scalar
singlets and additional quark and lepton singlets including right-handed and
Majorana neutrinos, is used to determine the contributions to the electron and
muon Electric Dipole Moment. The additional CP violation sources come from the
lepton sector, where neutrino masses are explained by an Inverse Seesaw
Mechanism and the CP violating phase of the PMNS matrix generates complex
interactions that involves exotic neutrino and sneutrino mass eigenstates. Such
contributions are studied at one and two-loop level by considering the
associated Barr-Zee diagrams and their supersymmetric counterpart. At one-loop
level, it is found that the Electric Dipole Moment fixes a relationship between
chargino and sneutrino masses depending on which particles have a mass bellow
$10^{6}$ GeV. At two loop level, contributions are comparable to the one-loop
contributions but the integrals diverge in some cases, yielding additional
restrictions such as no degenerate sneutrino masses and they should be heavier
than chargino masses.
