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We analyze the correlations between electric dipole moments (EDMs) of theneutron and heavy atoms and CP violation in B_{s,d} mixing in two Higgs doubletmodels respecting the Minimal Flavour Violation hypothesis, with flavour-blindCP-violating (CPV) phases. In particular, we consider the case of flavour-blindCPV phases from i) the Yukawa interactions and ii) the Higgs potential. We showthat in both cases the upper bounds on the above EDMs do not forbid sizablenon-standard CPV effects in B_s mixing. However, if a large CPV phase in B_smixing will be confirmed, this will imply EDMs very close to their presentexperimental bounds, within the reach of the next generation of experiments, aswell as BR(B_{s,d}-> mu^+ mu^-) typically largely enhanced over its SMexpectation. The two flavour-blind CPV mechanisms can be distinguished throughthe correlation between S_psi K_S and S_psi phi that is strikingly different ifonly one of them is relevant. Which of these two CPV mechanisms dominatesdepends on the precise values of S_psi phi and S_psi K_S, as well as on the CKMphase (as determined by tree-level processes). Current data seems to show amild preference for a hybrid scenario where both these mechanisms are at work.

EDMs vs. CPV in B_{s,d} mixing in two Higgs doublet models with MFV