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