  CP violation in the third generation fermion Higgs couplings may play an
important role in the electroweak baryogenesis, however it is strongly bounded
by the experimental limits on the electron electric dipole moment. In the
effective field theory framework to beyond the Standard Model physics, it can
originate from dimension six operators. Under such assumptions like Minimal
Flavour Violation or flavour symmetries, the Wilson coefficients of those
operators have in general certain flavour structure. In that case the imaginary
parts of the $h\tau\tau$ and $hee$ couplings are linked to each other. We point
out that due to the very strong bound from the electron electric dipole moment
on the imaginary part of $hee$ coupling, the bound on the imaginary part of the
$h\tau\tau$ coupling is then generically two orders of magnitude stronger than
the one obtained from the $\tau$-loop contributions to the Barr-Zee diagram. We
briefly discuss the potential impact of this fact on the electroweak
baryogenesis.
