  The determination of the CP nature of the Higgs coupling to top quarks is
addressed in this paper, using $t{\bar t} h$ events produced in $\sqrt{s} = 13$
TeV proton-proton collisions at the LHC. Dileptonic final states are employed,
with two oppositely charged leptons and four jets, corresponding to the decays
$t\rightarrow bW^+ \rightarrow b \ell^+\nu_\ell$, $\bar{t}\rightarrow
\bar{b}W^- \rightarrow \bar{b} \ell^-\bar{\nu}_\ell$ and $h\rightarrow
b\bar{b}$. Pure scalar ($h=H$), pure pseudo-scalar ($h=A$) and CP-violating
Higgs boson signal events, generated with MadGraph5_aMC@NLO, are fully
reconstructed through a kinematic fit. We furthermore generate samples that
have both a CP-even and a CP-odd component in the $t \bar t h$ coupling in
order to probe the ratio of the two components. New angular distributions of
the decay products, as well as CP angular asymmetries, are explored in order to
separate the scalar from the pseudo-scalar components of the Higgs boson and
reduce the contribution from the dominant irreducible background, $t{\bar
t}b{\bar b}$. Significant differences between the angular distributions and
asymmetries are observed, even after the full kinematic fit reconstruction of
the events, allowing to define the best observables for a global fit of the
Higgs couplings parameters.
