We investigate rare decays of tau leptons that occur via exchange of heavy on -shell neutrinos N-j (j =1,2). These neutrinos can be either Dirac or Majorana, and are considered to be almost degenerate in mass. The decays can thus be either lepton number conserving (LNC), tau(-/+) -> pi N--/+(j) -> pi(-/+)mu(-/+)pi(+/-), or lepton number violating (LNV), tau(-/+) -> pi N--/+(j) -> pi(-/+)mu(+/-)pi(-/+). If neutrinos are Dirac, only LNC decays are possible. If they are Majorana, both LNC and LNV are possible. We derive the corresponding expressions for the effective decay widths Gamma((X)) (eff,-/+) (X=LNC, LNV) of these rare decays, where we account for N-1 -N-2 overlap and oscillation effects and for the finite detector length effects. We then numerically evaluate these decay widths as well as the related CP violation asymmetry width triangle Gamma((X))(CP) = (Gamma((X))(eff) ,- - Gamma((X))(eff,+)). We conclude that for certain, presently allowed, ranges of the heavy -light neutrino mixing parameters, such decays and asymmetries could be observed in Belle II experiment.