  We present results from archival Very Large Array (VLA) data and new VLA
observations to investigate the long term behavior of the circular polarization
of M81*, the nuclear radio source in the nearby galaxy M81. We also used the
Berkeley-Illinois-Maryland Association (BIMA) array to observe M81* at 86 and
230 GHz. M81* is unpolarized in the linear sense at a frequency as high as 86
GHz and shows variable circular polarization at a frequency as high as 15 GHz.
The spectrum of the fractional circular polarization is inverted in most of our
observations. The sign of circular polarization is constant over frequency and
time. The absence of linear polarization sets a lower limit to the accretion
rate of $10^{-7} M_\odot y^{-1}$. The polarization properties are strikingly
similar to the properties of Sgr A*, the central radio source in the Milky Way.
This supports the hypothesis that M81* is a scaled up version of Sgr A*. On the
other hand, the broad band total intensity spectrum declines towards milimeter
wavelengths which differs from previous observations of M81* and also from Sgr
A*.
