  We use the associated production of top-quark pairs with a generic scalar
boson at the LHC to explore the sensitivity of a large set of observables to
the sign of the CP mixing angle, present in the coupling between the scalar
boson and the top quarks. The mass of the scalar boson is set to $m_{\phi}=125$
GeV and its coupling to top-quarks is varied such that $\alpha=$ 0$^\circ$,
22.5$^\circ$, 45.0$^\circ$, 67.5$^\circ$, 90.0$^\circ$, 135.0$^\circ$ and
180.0$^\circ$. Dileptonic final states of the $t\bar{t}\phi$ system are used,
with the scalar boson decaying as $\phi\rightarrow b\bar{b}$. A new method to
reconstruct the scalar mass, originally designed for the low mass regime is
used, improving the resolution of the Higgs mass by roughly a factor of two. A
full phenomenological analysis is performed using Standard Model background and
signal events generated with MadGraph5aMC@NLO and reconstructed using a
kinematical fit. The most sensitive CP-observables are selected to compute
Confidence Level (CL) limits as a function of the sign of the top quark Yukawa
couplings to the scalar boson. We also explore the sensitivity to interference
terms using differential distributions and angular asymmetries. Given the
significant difference between the pure scalar and pure pseudo-scalar
production cross section values, it is unlikely the $t\bar{t}\phi$ channel
alone will be sensitive to the sign of the CP-mixing angle or interference
terms, even at the end of the LHC. Using the $b_2^{t\bar{t}\phi}$ and
$b_4^{t\bar{t}\phi}$ variables, exclusion limits at 95\% CL for the CP-even and
CP-odd components of the top quark Yukawa couplings are expected to be set to
$\tilde{\kappa} \in$ [-0.698,+0.698] and $|\kappa| \in$ [0.878,1.04],
respectively, at the end of the High Luminosity phase of the LHC (HL-LHC) by
using the dileptonic decay channel alone.
