In the presence of an electric dipole coupling of$$\overline {tt} $$ to a photon, and an analogous ‘weak’ dipole coupling to the Z, CP violation in the process e⁺e⁻ →$$\overline {tt} $$ results in modified polarization of the top and the anti-top. This polarization can be analyzed by studying the angular distributions of decay charged leptons when the top or anti-top decays leptonically. Analytic expressions are presented for these distributions when eithert or$$\overline t $$ decays leptonically, including$$\mathcal{O}$$(α_s) QCD corrections in the soft-gluon approximation. The angular distributions are insensitive to anomalous interactions in top decay. Two types of simple CP-violating polar-angle asymmetries and two azimuthal asymmetries, which do not need the full reconstruction of thet or$$\overline t $$, are studied. Independent 90% CL limits that may be obtained on the real and imaginary parts of the electric and weak dipole couplings at a linear collider operating at √ s = 500 GeV with integrated luminosity 500 fb⁻ and also at √s = 1000 GeV with integrated luminosity 1000 fb⁻ have been evaluated. The effect of longitudinal electron and/or positron beam polarizations has been included.