Study of CMS sensitivity to neutrinoless $\tau$ decay at LHC

The Large Hadron Collider (LHC), scheduled to start operation in 2006, is foreseen to provide in the first year of running a total of $\sim 10^{12}$ $\tau$ leptons. CMS (Compact Muon Solenoid) is a general-purpose experiment designed to study proton-proton and heavy-ion collisions at LHC. Even if the Susy particles and Higgs searches togheter with the B-physics present its main goal, the large amount of $\tau$-lepton, could allow a systematic study of tau-physics. We have performed a full simulation of CMS using GEANT 3 package and the object-oriented reconstruction program ORCA to study the sensitivity to neutrinoless tau decay $\tau \to \mu^+ \mu^- \mu^-$ and $\tau \to \mu \gamma$. We present the analysis developed for these channels and the results obtained.