  We propose a method for determining the CP nature of a neutral Higgs boson or
spin-zero resonance $\phi$ at the CERN Large Hadron Collider (LHC) in its
$\phi\to\tau^{-}\tau^{+}$ decay channel. The method can be applied to any
1-prong $\tau$-decay mode, which comprise the majority of the $\tau$-lepton
decays. The proposed observables allow to discriminate between pure scalar and
pseudoscalar Higgs-boson states and/or between a CP-conserving and CP-violating
Higgs sector. We show for the decays $\tau\to\pi\nu_{\tau}$ that the method
maintains its discriminating power when measurement uncertainties are taken
into account. The method will be applicable also at a future linear
$e^{+}e^{-}$ collider.
