  We examine the CP-conserving (CPC) and CP-violating (CPV) effects of a
general HZZ coupling through a study of the process H -> ZZ* -> 4 leptons at
the LHC. We construct asymmetries that directly probe these couplings. Further,
we present complete analytical formulae for the angular distributions of the
decay leptons and for some of the asymmetries. Using these we have been able to
identify new observables which can provide enhanced sensitivity to the CPV $H
ZZ$ coupling. We also explore probing CP violation through shapes of
distributions in different kinematic variables, which can be used for Higgs
bosons with mH < 2 mZ.
