  The contributions of a second Higgs doublet to the electron electric dipole
moment near the heavy Higgs decoupling limit are determined within an effective
field theory framework. In models that satisfy the Glashow-Weinberg condition,
the leading contributions in this limit at effective dimension six are shown to
come from two-loop Barr-Zee diagrams that include the Standard Model-like Higgs
boson. Additional diagrams that include heavy Higgs bosons are sub-leading and
contribute only at effective dimension eight near the decoupling limit. This
simplification implies that to leading order in this limit, contributions of a
second Higgs doublet to the electron electric dipole moment can be couched
entirely in terms of the ratio of Higgs doublet expectation values and a single
universal phase appearing in the effective couplings of the Standard Model-like
Higgs boson to fermions, without direct reference to the heavy Higgs boson
masses or couplings. The recent bound from the ACME II experiment constrains
the phases of the couplings of the Standard Model-like Higgs boson to up-type
quarks and leptons at the part per mil level in Type I and IV two Higgs doublet
models. In Type II and III models these phases are constrained at the two parts
per mil or better level except in a tiny sliver of parameter space with nearly
equal Higgs doublet expectation values where destructive interference among
contributing diagrams happens to occur. In a more general phenomenological
parameterization with individual effective phases in the couplings of the
Standard Model-like Higgs boson to third generation fermions and the electron,
the top quark and electron coupling phases are constrained at the part per mil
level except in tiny slivers of parameter space, while the bottom quark and
tau-lepton coupling phases are constrained only at the thirty percent level.
