  We analyze the $\tau^-\to(K\pi)^-\nu_\tau$ decays within an effective field
theory description of heavy new physics (NP) modifying the SM left-handed weak
charged current and include refined SM input for the participant meson form
factors exploiting chiral symmetry, dispersion relations and (lattice) data. We
include the leading dimension six operators and work at linear order in the
effective couplings. Within this setting we:
  i) follow the derivation in Phys. Rev. Lett. 120 (2018) no.14, 141803 where
it was proved unambiguously that it is impossible to understand the BaBar
anomaly in the CP asymmetry measurement within this framework. We allow for
reasonable variations of the hadronic input involved and study the associated
uncertainty;
  ii) first show that the anomalous bump present in the published Belle data
for the $K_S\pi^-$ invariant mass distribution close to threshold cannot be due
to heavy NP;
  iii) first bind the heavy NP effective couplings using
$\tau^-\to(K\pi)^-\nu_\tau$ decays and show that they are competitive with
those found in hyperon semileptonic decays (but clearly not with those obtained
in Kaon (semi)leptonic decays for NP scalar currents). We put forward that the
comparison of the considered tau decays with (semi)leptonic kaon and hyperon
decays provide with meaningful tests of lepton universality for (NP) tensor
interactions.
  We also compare the SM predictions with the possible deviations caused by NP
in a couple of Dalitz plot distributions, in the forward-backward asymmetry and
in the di-meson invariant mass distribution and discuss the most interesting
measurements to be performed at Belle-II using these decays data.
