Abstract : Results are presented on a search for a light charged Higgs boson that can be produced in the decay of the top quark to charged H and b quark and which, in turn, decays into tau and tau neutrino. The analysed data correspond to an integrated luminosity of about 2 inverse femtobarns recorded in proton-proton collisions at sqrt(s) = 7 TeV by the CMS experiment at the LHC. The search is sensitive to the decays of the top quark pairs t anti-t to charged Higgs W b anti-b and t anti-t to charged Higgs b anti-b. Various final states have been studied separately, all requiring presence of a tau lepton from charged Higgs decays, missing transverse energy, and multiple jets. Upper limits on the branching fraction B(t to charged Higgs b) in the range of 2-3% are established for charged Higgs boson masses between 80 and 160 GeV, under the assumption that B(charged Higgs to tau anti-tau neutrino) = 1.