If neutral Higgs bosons will be discovered at the CERN Large Hadron Collider (LHC) then an important subsequent issue will be the investigation of their CP nature. Higgs boson decays into τ lepton pairs are particularly suited in this respect. Analyzing the three charged pion decay modes of the τ leptons and taking expected measurement uncertainties at the LHC into account, we show that the CP properties of a Higgs boson can be pinned down with appropriately chosen observables, provided that sufficiently large event numbers will eventually be available.

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