  Current data on the signal strengths and angular spectrum of the 125.5 GeV
Higgs boson still allow a CP-mixed state, namely, the pseudoscalar coupling to
the top quark can be as sizable as the scalar coupling: $C_u^S \approx C_u^P
=1/2$. CP violation can then arise and manifest in sizable electric dipole
moments (EDMs). In the framework of two-Higgs-doublet models, we not only
update the Higgs precision (Higgcision) study on the couplings with the most
updated Higgs signal strength data, but also compute all the Higgs-mediated
contributions from the 125.5 GeV Higgs boson to the EDMs, and confront the
allowed parameter space against the existing constraints from the EDM
measurements of Thallium, neutron, Mercury, and Thorium monoxide. We found that
the combined EDM constraints restrict the pseudoscalar coupling to be less than
about $10^{-2}$, unless there are contributions from other Higgs bosons,
supersymmetric particles, or other exotic particles that delicately cancel the
current Higgs-mediated contributions.
