  Motivated by models proposed to explain the Standard Model anomalies, and the
unprecedented $\tau^{+}\tau^{-}$ data to be collected by the Belle~II
experiment during the next years, we study the kinematics of tau pair decays
and propose a new method to search for lepton flavor violating processes in tau
lepton decays to invisible beyond Standard Model particles, such as $\tau \to
\ell \alpha$, where $\ell$ is either an electron or a muon, and $\alpha$ is a
massive particle that escapes undetected. The new method improves by one order
of magnitude the expected upper limit on the $\tau \to \ell \alpha$ production
in 3x1 prong tau decays and establishes the possibility of performing this
search in 1x1 prong tau decays which has not been previously considered.
