  We listed all possible dimension-six CP-violating $SU_c(3)\times
SU_L(2)\times U_Y(1)$ invariant operators involving the third-family quarks,
which can be generated by new physics at a higher energy scale. The expressions
of these operators after electroweak symmetry breaking and the induced
effective couplings $Wt\bar b$, $Xb\bar b$ and $Xt\bar t$ $(X=Z,\gamma,g,H)$
are also presented. We have evaluated sample contributions of these operators
to CP-odd asymmetries of transverse polarization of top quark in single top
production at the upgraded Tevatron, the similar effect in top-antitop pair
production at the NLC, and the CP-odd observables of momentum correlations
among the top quark decay products at the NLC. The energy and luminosity
sensitivity in probing these CP-violating new physics has also been studied.
