  We conducted a Very Large Array survey of eleven low luminosity active
galactic nuclei for linear and circular polarization at 8.4 GHz. We detected
circular polarization in one source (M81*) and linear polarization in 3
sources. Sensitivity limits were ~0.1% for both modes of polarization in 9 of
11 sources. The detections confirm the importance of nonthermal emission in
LLAGN. However, detection rates for circular and linear polarization are lower
for these sources than for more powerful AGN. Fractional linear polarization in
detected sources is also lower than in more powerful AGN. The weak linear
polarization in the survey sources indicates their overall similarity to Sgr
A*. Confusion with thermal sources, depolarization and weaker, less extended
jets may contribute to these differences. We detect a rotation measure >~ 7 x
10^4 rad m^-2 for NGC 4579. This may arise from magnetized plasma in the
accretion, outflow or interstellar regions. Inverted spectra are present in
both M81* and Sagittarius A* and absent from all sources in which circular
polarization is not detected. This suggests that optical depth effects are
important in the creation of circular polarization.
