  Models of the resolved Event Horizon Telescope (EHT) sources Sgr A* and M87*
are constrained by observations at multiple wavelengths, resolutions,
polarizations, and time cadences. In this paper we compare unresolved circular
polarization (CP) measurements to a library of models, where each model is
characterized by a distribution of CP over time. In the library we vary the
spin of the black hole, the magnetic field strength at the horizon (i.e. both
SANE and MAD models), the observer inclination, a parameter for the maximum
ion-electron temperature ratio assuming a thermal plasma, and the direction of
the magnetic field dipole moment. We find that ALMA observations of Sgr A* are
inconsistent with all edge-on ($i = 90^\circ$) models. Restricting attention to
the magnetically arrested disk (MAD) models favored by earlier EHT studies of
Sgr A*, we find that only models with magnetic dipole moment pointing away from
the observer are consistent with ALMA data. We also note that in 26 of the 27
passing MAD models the accretion flow rotates clockwise on the sky. We provide
a table of the mean and standard deviation of the CP distributions for all
model parameters along with their trends.
