This thesis describes the search for the Standard Model Higgs boson decaying to tau lepton pairs, in the Tevatron proton-antiproton collisions at a center of mass energy $\sqrt{s}$ = 1.96 TeV. The search is based on approximately 2.3 fb$^{-1}$ of CDF Run II data and is performed by considering the following signal processes: WH($\rightarrow\tau\tau$), ZH($\rightarrow\tau\tau$), qHq'$\rightarrow$q$\tau\tau$q' and gg$\rightarrow$H$\rightarrow\tau\tau$. Events are selected by requiring an hadronic tau and one isolated electron or muon, coming from the leptonic decay of one of the two taus. In addition, at least one calorimeter jet must be present in the final state. We expect 921.8$\pm$48.9 background events in the 1 jet channel and 159.4$\pm$11.6 in the $\ge$ 2 jets channel, while in data we observe 965 and 166 events, respectively. In order to improve the search sensitivity we employ a multivariate technique, based on a set of Boosted Decision Trees trained to get the best sep aration between signal and the dominant sources of background. We observe no evidence for a Higgs boson signal and therefore we set a 95\% confidence level (C.L.) upper limit on the cross section relative to the SM predictions ($\sigma/\sigma_{\mathrm{SM}}$). Results are presented for the Higgs boson mass varying from M$_\mathrm{H}$ = 100 GeV/$c^2$ to M$_\mathrm{H}$ = 150 GeV/$c^2$. For the mass hypothesis of 120 GeV/c$^2$ the observed limit is 27.2, while the corresponding expected value is 23.4$^{+9.8}_{-6.4}$.