  In the work presented here, we have studied the impact of right handed
neutrinos, which are introduced to account for the evidence of neutrino masses,
on charged lepton flavour violating observables. In particular, we have focused
on the loop induced decays of the Z boson into two leptons of different
flavour. We have performed a numerical study of the rates predicted for these
processes within the Inverse Seesaw model, specifically considering scenarios
where $ \mu -e $ transitions are suppressed. Our conclusion, after comparison
with the most relevant experimental constraints, is that branching ratios as
large as $ 10^{-7} $ can be predicted in the $ \tau -\mu $ or $ \tau -e $
channels, together with heavy neutrinos having masses of the TeV order. Such
rates could be accessible at next generation colliders.
