Motivated by the evidence of physics beyond the Standard Model, the unprecedented amount of tau pairs to be collected by the Belle II experiment in the coming years, and inspired by previous proposals, we present an study of the kinematics of tau pair decays and propose a new method to search for lepton flavour violating processes in tau lepton decays to invisible beyond Standard Model particles, such as 𝜏 → ℓ𝛼, where ℓ is either an electron or a muon, and 𝛼 is a massive undetectable particle. Application of our method leads to an improvement by one order of magnitude the expected upper limit on the 𝜏 → ℓ𝛼 production in 3x1 prong tau decays.