Lepton flavor violated process are strongly suppressed in the Standard Model due to very small neutrino mass, but can be sizable in some extended models. The current experimental bounds on decay modes ± → a ± are much weaker than other flavor violated processes because of the huge irreducible backgrounds → ν ν . In this paper, we give the full helicity density matrix of both the signal and backgrounds, and then study polarization effects. Particularly, we treat inclusively the two missing neutrinos in the background, and we find that both longitudinal and transverse polarization effects survives even the relative kinematical degrees of freedom of the two neutrinos are integrated out. Furthermore, we have show that signal and backgrounds have distinctive polarization effects which can be measured by using energy fractions of the charged decay products. This is particularly useful because kinematical reconstruction is not required. In case of that the decaying lepton is not polarized, we show that correlations between polarizations of lepton pair generated at colliders are still useful to search for the signals. More interestingly, polarization correlations depends on product of scalar and pseudo-scalar ALP couplings, and hence are sensitive to their relative sign. We demonstrate that how the polarization correlation effects can be used to investigate flavor violating decays τ ± → a ± at the BelleII experiment.