  Extended scalar sectors with additional degrees of freedom appear in many
scenarios beyond the Standard Model. Heavy scalar resonances that interact with
the neutral current could be discovered via broad resonances in the tails of
the four-lepton invariant mass spectrum, where the Standard Model background is
small and well understood. In this article we consider a recent ATLAS
measurement of four-lepton final states, where the data is in excess over the
background for invariant masses above 500 GeV. We discuss the possibility that
this excess could be interpreted as a "double peak" from the two extra heavy
neutral scalars of a CP violating Two Higgs Doublet Model, both coupling to the
$Z$ boson. We apply an iterative fitting procedure to find viable model
parameters that can match the excess, resulting in a benchmark point where the
observed four-lepton invariant mass spectrum can be explained by two scalar
particles $H_2$ and $H_3$, with masses of 540 GeV and 631 GeV, respectively,
being admixtures of the CP eigenstates. Our explanation predicts additional
production processes for $t\bar t$, $W^+W^-$, $4b$ and $\gamma\gamma$, some of
which have cross sections close to the current experimental limits. Our results
further imply that the electric dipole moment of the electron should be close
to the present bounds.
