  We provide a detailed, model-independent, study for CP violation effects due
to the T-odd top-quark electric dipole moment (EDM) and weak dipole moment
(WDM) in the top-quark pair production via $e^+e^-$ and two-photon annihilation
at a next $e^+e^-$ linear collider (NLC). There are two methods in detecting CP
violation effects in these processes. One method makes use of measurements of
various spin correlations in the final decay products of the produced top-quark
pair, while the other is to measure various CP-odd polarization asymmetry
effects of the initial states. In the $e^+e^-$ case only the first method can
be used, and in the $\gamma\gamma$ case both methods can be employed. We
provide a complete classification of angular correlations of the $t$ and
$\bar{t}$ decay products under CP and CP\tilde{T} which greatly faciliate CP
tests in the $e^+e^-$ mode. Concentrating on the second method with the Compton
back-scattered high-energetic laser light off the electron or positron beam in
the two-photon mode, we construct two CP-odd and CP\tilde{T}-even initial
polarization configurations and apply them to investigating CP-violating
effects due to the top-quark EDM. With a typical set of experimental parameters
at the NLC, we compare the 1-\sigma sensitivities to the top-quark EDM and WDM
in the $e^+e^-$ mode and the two-photon mode. Some model expectation values of
the T-odd parameters are compared with the results.
