  We compare the impact of top-quark spin polarization effects in Higgs boson
production in association with top-quark pairs and in corresponding backgrounds
at the LHC. Because of the spin-zero nature of the Higgs boson, one expects, in
the chiral limit for the top quarks, a substantial complementarity in $t\bar t$
spin correlations for a Higgs decaying into fermions/gauge-bosons and
$t\bar{t}$ spin correlations for the corresponding irreducible $t\bar t f\bar
f/VV$ backgrounds. Although top mass effects in $t\bar t H$ production are in
general dominant, and seriously spoil the chiral-limit expectations, one can
find observables that capture the $t \bar t$ angular spin correlations and can
help in separating the signal from irreducible backgrounds. In particular, we
show that, for both $H\to b\bar b$ and $H\to \gamma\gamma$, taking into account
$t\bar{t}$ spin correlations in $t\bar t H$ production and irreducible
backgrounds could appreciably improve the LHC sensitivity to the $t\bar t H$
channel.
