  A striking manifestation of CP violation in the electroweak symmetry breaking
sector would be the existence of neutral Higgs boson(s) with undefined CP
parity. We analyse signatures of such a boson, with a mass of about 300 GeV or
larger, produced in high energy proton-proton collisions at LHC energies in its
top-quark antitop-quark decay channel. The large irreducible $t\bar t$
background is taken into account. We propose, both for the dilepton and the
lepton + jets decay channels of $t\bar t$, several correlations and asymmetries
with which (Higgs sector) CP violation can be traced. We show that for
judiciously chosen cuts on the $t\bar t$ invariant mass these CP observables
yield, for an LHC integrated luminosity of 100 $\rm{fb}^{-1}$, statistically
significant signals for a range of Higgs boson masses and Yukawa couplings.
