  The process of top-quark pair production at future high-energy $e^+ e^-$
linear colliders has been investigated as a possible test of physics beyond the
Standard Model. Non-standard interactions have been assumed both for the
production and for the subsequent decay of the top quarks. The energy spectrum
of the single lepton $l^\pm$ and the energy correlation of $l^+$ and $l^-$
emerging from the process $e^+e^-\to t\bar{t}\to l^\pm X/l^+l^-X$ are
calculated. The energy- spectrum asymmetry of $l^+$ and $l^-$ is considered as
a measure of CP violation. An optimal method to determine whether CP violation
occurs in the production or in the decay processes is proposed.
