We discuss the effect of CP violation in the aligned scenario of the general two-Higgs-doublet model, in which the Higgs potential and the Yukawa interaction provide additional CP-violating phases. An alignment is imposed to the Yukawa interaction in order to avoid dangerous flavor changing neutral currents. The Higgs potential is also aligned such that the coupling constants of the lightest Higgs boson, which is identified as the discovered Higgs boson with the mass of 125 GeV, are the same as those of the standard model. In general, CP-violating phases originated by the Yukawa interaction and the Higgs potential are strongly constrained by the current data for the electric dipole moment (EDM). It is found that in our scenario contributions from the two sources of CP violation can be destructive and consequently their total contribution can satisfy the EDM results, even when each CP-violating phase is large. Such a large CP-violating phase can be tested at collider experiments by looking at the angular distributions of particles generated by the decays of the additional Higgs bosons.

We study how effects of the CP violation can be observed indirectly by precision measurements of Higgs boson couplings at a future Higgs factory such as the international linear collider. We consider two Higgs doublet models with the softly broken discrete symmetry. We find that by measuring the Higgs boson couplings very precisely we are able to distinguish the two Higgs doublet model with CP violation from the CP conserving one.

We discuss the testability of CP-violating phases at future lepton colliders for the scenario which satisfies electric dipole moment data by destructive interferences among several phases. We consider the general but aligned two Higgs doublet model which has the CP-violating phases in the Higgs potential and the Yukawa interaction. The Yukawa interaction terms are aligned to avoid flavor changing neutral currents at tree level. The Higgs potential is also aligned such that the coupling constants of the lightest Higgs boson with the mass of 125 GeV to the Standard Model (SM) particles are the same as those of the SM at tree level. We investigate the azimuthal angle distribution of the hadronic decay of tau leptons arising from production and decay of the extra Higgs bosons, which contains information of the CP-violating phases. From the signal and background simulation, we find that the scenario with finite CP-violating phases can be distinguished from CP conserving one at future lepton colliders like the International Linear Collider.