  The possibility to discriminate between different operators contributing to
lepton flavour violating tau decays is discussed within an effective field
theory framework. Correlations among decay rates in different channels as well
as differential distributions in many-body decays are considered. Recent
developments in the determination of the hadronic form factors for $\tau
\rightarrow \ell \pi \pi$ ($\ell = e, \mu$) decays are incorporated in the
analysis. The above issues are exemplified by considering a Higgs-like boson
with lepton flavour violating couplings. Implications of the search for lepton
flavour violating Higgs decays performed recently by the CMS collaboration are
also discussed.
