We analyze the constraints on a CP-violating, flavor conserving, two Higgs
doublet model from the measurements of Higgs properties and from the search for
heavy Higgs bosons at LHC, and show that the stronger limits typically come
from the heavy Higgs search channels. The limits on CP violation arising from
the Higgs sector measurements are complementary to those from EDM measurements.
Combining all current constraints from low energy to colliders, we set generic
upper bounds on the CP violating angle which parametrizes the CP odd component
in the 126 GeV Higgs boson.Comment: 34 pages, 17 figures, 2 tables; references added, constraints from
Higgs decay into tau updated, version accepted for publication in JHE
