  We explore $\mathcal CP$-violation effects of Higgs-top interactions in the
associated production of a Higgs boson with top-pair in the dileptonic decay
modes of top-quark originating from proton proton collisions $pp \to t\bar{t}H
\to (l^+ \nu_l b)(l^{-} \bar{\nu_l} \bar{b})H$ at NLO in QCD matched to parton
shower via T-odd observables using momenta of various particles involved in the
process. In particular, we predict the constraints on the $\mathcal
CP$-violating $t\bar{t}H$ coupling obtained through the production asymmetries
associated with the T-odd observables in the dileptonic decay channel of the
$t\bar{t}$ pair for the LHC with centre-of-mass energy of 13 TeV and an
integrated luminosity of 139 fb$^{-1}$. We also present the corresponding
limits for future hadron colliders, namely the High Luminosity LHC (HL-LHC) and
the Future Circular Collider (FCC-HH). Our estimates of the $t\bar{t}H$
interaction strength reveal that the upper bound on pseudoscalar coupling $c_p$
corresponding to the largest asymmetry would be of about $1.96 \times 10^{-2}$
at 2.5$\sigma$ C.L. for $c_s$ = 1 at the LHC with $\sqrt{S}$ = 13 TeV for an
integrated luminosity of 139 fb$^{-1}$. The respective limits for HL-LHC and
FCC-hh with the projected Luminosities of 3 ab$^{-1}$ and 30 ab$^{-1}$ are
found to be to $3.4\times 10^{-3}$ and $1.6\times 10^{-4}$ respectively at
2.5$\sigma$ C.L.
