This thesis presents the search for a charged-lepton flavour violation via a model-independent Higgs-like boson decaying to a muon and a tau lepton, H→μτ. The validation of high-pT tau lepton identification is performed with the measurement of Z→τ+τ− production cross-section, using 2\;fb−1 of integrated luminosity from pp collisions at s=8 TeV collected by the LHCb experiment at the LHC in 2012. The tau leptons are reconstructed in both leptonic and hadronic decay channels. The cross-section, restricted to events with both tau leptons having a transverse momentum greater than 20 GeV/c and a pseudorapidity between 2 and 4.5, and with a tau pair invariant mass between 60 and 120 GeV/c2, is measured to be \sigma_{Z\rightarrow\tau^+\tau^-}} = 95.20 \pm 2.13 \pm 4.79 \pm 0.17 \pm 1.10 \pb. The uncertainties are statistical, systematic, from the LHC beam energy, and from the integrated luminosity. The results are compatible with the lepton universality hypothesis in Z decays, and are in agreement with NNLO Standard Model predictions. Using the validated tau-lepton identification and detection efficiencies, the search for H→μτ covering 99\% of tau decay modes found no statistically significant excess. The upper limit on the cross-section times branching fraction, \sigma_{gg\rightarrow H\rightarrow\mu\tau, at 95\% confidence level is set, ranging from about 22 pb for mH=45 GeV/c2 to 4 pb at 195 GeV/c2. Assuming the Standard Model Higgs, the limit on the braching fraction is B(H→μτ)<25.7%, corresponding to a Yukawa coupling of ∣Yμτ∣2+∣Yτμ∣2<1.69×10−2