  In this paper we investigate methods to study the $t\bar{t}$ Higgs coupling.
The spin and CP properties of a Higgs boson are analysed in a model-independent
way in its associated production with a $t\bar{t}$ pair in high-energy $e^+e^-$
collisions. We study the prospects of establishing the CP quantum numbers of
the Higgs boson in the CP-conserving case as well as those of determining the
CP-mixing if CP is violated. We explore in this analysis the combined use of
the total cross section and its energy dependence, the polarisation asymmetry
of the top quark and the up-down asymmetry of the antitop with respect to the
top-electron plane. We find that combining all three observables remarkably
reduces the error on the determination of the CP properties of the Higgs Yukawa
coupling. Furthermore, the top polarisation asymmetry and the ratio of cross
sections at different collider energies are shown to be sensitive to the spin
of the particle produced in association with the top quark pair.
