  In a scattering experiment, the induced dipole moments of a magnetoelectric
point scatterer in response to driving fields are given by its polarizability
tensor \alpha. Its linewidth will be dictated by the local density of optical
states (LDOS) at the scatterer's position. To retrieve the magnetoelectric
cross coupling components of \alpha for an archetypical magnetoelectric
scatterer - a split ring resonator - we study the frequency dependent
extinction cross section as a function of distance to an interface. Rather than
following a purely electric or purely magnetic LDOS, we find a dependence which
reflects the interplay of both dipole moments in a 'mixed' magnetoelectric
LDOS. For a strongly magnetoelectric cross-coupled microwave scatterer, we
compare analytical point dipole with finite element method calculations.
