  It is well known that $CP$-violating coupling of the Yukawa interaction of
top-quark is a promising candidate of a new source of $CP$ violation effect.
Precisely measurement of its $CP$ properties is crucial for understanding new
physics above the electroweak scale. In this paper, we introduce a complete
analysis method for probing $CP$ violation effects in the associated production
of top-quark pair and Higgs boson at $e^{-}e^{+}$ collider. Reconstructions of
the top-quarks are not needed in our strategy. The observables are defined
based on spin correlation effects of the leptons emerging from decays of
top-quarks, and their formal expressions are universal at any reference frames.
Two reference frames, the rest frame of the top-quark pair and the rest frame
of Higgs boson, are examined. Importantly, large enhancement effects for both
$CP$-odd and $CP$-even observables are observed in the rest frame of Higgs
boson. This can be essential for probing $CP$ violation effects at future
$e^{-}e^{+}$ collider.
