  CP-violating contributions to Higgs--fermion couplings are absent in the
standard model of particle physics (SM), but are motivated by models of
electroweak baryogenesis. Here, we employ the framework of the SM effective
theory (SMEFT) to parameterise deviations from SM Yukawa couplings. We present
the leading contributions of the relevant operators to the fermionic electric
dipole moments (EDMs). We obtain constraints on the SMEFT Wilson coefficients
from the combination of LHC data and experimental bounds on the electron,
neutron, and mercury EDMs, and for the first time, we perform a combined fit to
LHC and EDM data allowing the presence of CP-violating contributions from
several fermion species simultaneously. Among other results, we find
non-trivial correlations between EDM and LHC constraints even in the
multi-parameter scans, for instance, when floating the CP-even and CP-odd
couplings to all third-generation fermions.
