  In a bottom-up approach we investigate lepton-flavour violating processes
$\tau \to 3 \ell$ that are mediated by New Physics encoded in effective-theory
operators of dimension six. While the opportunity to scrutinize the underlying
operator structure has been investigated before, we explore the benefits of
utilising the polarization direction of the initial $\tau$ lepton and the
angular distribution of the decay. Given the rarity of these events (if
observed at all), we focus on integrated observables rather than spectra, such
as partial rates and asymmetries. In an effort to estimate the number of events
required to extract the coupling coefficients to the effective operators we
perform a phenomenological study with virtual experiments.
