Top quark with its large Yukawa coupling is crucially important to explore TeV scale physics. Therefore, the study of Higgs-top sector is highly motivated to look for any deviations from the standard model predictions. The most general lowest order Lagrangian for the Higgs-top Yukawa coupling has scalar ($��$) and pseudoscalar ($\tilde��$) components. Currently, these couplings are constrained indirectly using the present experimental limits on the Higgs-$��$-$��$ and Higgs-gluon-gluon couplings. Furthermore, stronger bounds on $��$ and $\tilde��$ are obtained using the limits on the electric dipole moments (EDM). In this work, we propose an asymmetry-like observable $O_��$ in $t\bar{t}H$ production at the LHC to probe the Higgs-top coupling and to distinguish between the scalar and pseudoscalar components. We also show that the presence of the pseudoscalar component in the Higgs-top Yukawa coupling leads to a sizeable value for the top quark EDM. It is shown that a limit of $10^{-19}$ e.cm, which is achievable by the future $e^{-}e^{+}$ collider, allows us to exclude a significant region in the $(��,\tilde��)$ plane.

15 pages, 8 figures