The following calculations extend the results of the paper published on 1992 by K¨uhn and Mirkes (K&M), for the particular case of interference between an antisymmetric tensor and one (axial-)vector current. The KM analysis was based on a formalism designedto systematically handle reactions of the type τ → h1h2h3ντ , for h_{1,2,3} being any meson in the lighter SU(3) flavour octet, by considering the whole set of independent observable kinematical variables for these four body decays and singling out the case where the polarization of the lepton was actually measurable. On the other hand, the present work is based on the effective field theory study derived from introducing the most general non-standard interactions (NSI) between the light quarks and leptons at operator mass dimension six, including (pseudo)scalar, (axial)vector and tensor (absent in KM) lepton and hadron currents. Hence, the following results generalize K&M works encompassing the most gen- eral NSI and the celebrated KM formalism, which will allow us to study the most general new physics interactions in the considered decays systematically, including the full new physics dependence by handling the whole phase space. This is particularly promising concerning charge-parity and time-reversal viola- tion analyses.