  The Higgs sector of the Minimal Supersymmetric Extension of the Standard
Model may be described with a two Higgs doublet model with properties that
depend on the soft supersymmetry breaking parameters. For instance, flavor
independent CP-violating phases associated with the gaugino masses, the squark
trilinear mass parameters and the Higgsino mass parameter $\mu$ may lead to
sizable CP-violation in the Higgs sector. For these CP-violating effects to
affect the properties of the recently observed SM-like Higgs resonance, the
non-standard charged and neutral Higgs bosons masses must be of the order of
the weak scale, and both $\mu$ as well as the trilinear stop mass parameter
$A_t$ must be of the order or larger than the stop mass parameters. Constraints
on this possibility come from direct searches for non-standard Higgs bosons,
precision measurements on the lightest neutral Higgs properties, including its
mass, and electric dipole moments. In this article, we discuss these
constraints within the MSSM, trying to evaluate the possible size of the CP-odd
component of the lightest neutral Higgs boson, and the possible experimental
tests of this CP-violating effect at the LHC.
