  We study in detail the impact of anomalous Higgs couplings in angular
asymmetries of the crossing-symmetric processes H --> Zl+l- and e+e- --> HZ.
Beyond Standard Model physics is parametrized in terms of the
SU(3)xSU(2)_LxU(1)_Y dimension-six effective Lagrangian. In the light of
present bounds on d = 6 interactions we study how angular asymmetries can
reveal non-standard CP-even and CP-odd couplings. We provide approximate
expressions to all observables of interest making transparent their dominant
dependence on anomalous couplings. We show that some asymmetries may reveal BSM
effects that are hidden in other observables. In particular, CP-even and CP-odd
d = 6 HZgamma couplings as well as (to a lesser extent) HZll contact
interactions can generate asymmetries at the several percent level, while
having small or no effects on the di-lepton invariant mass spectrum of H -->
Zl+l-. Finally, the higher di-lepton invariant mass probed in e+e- --> HZ leads
to interesting differences in the asymmetries with respect to those of H -->
Zl+l- that may lead to complementary anomalous coupling searches at the LHC and
e+e- colliders.
