  We present a statistical analysis of polarized near-infrared (NIR) light from
Sgr A*, the radio source associated with the supermassive black hole at the
center of the Milky Way. The observations have been carried out using the
adaptive optics instrument NACO at the VLT UT4 in the infrared
$K_\mathrm{s}$-band from 2004 to 2012. Several polarized flux excursions were
observed during these years. Linear polarization at 2.2 $\mu m$, its statistics
and time variation, can be used constrain the physical conditions of the
accretion process onto this supermassive black hole. With an exponent of about
4 for the number density histogram of fluxes above 5~mJy, the distribution of
polarized flux density is closely linked to the single state power-law
distribution of the total $K_\mathrm{s}$-band flux densities reported earlier.
We find typical polarization degrees of the order of 20\%$\pm$10\% and a
preferred polarization angle of 13$^o$$\pm$15$^o$. Simulations show the
uncertainties under a total flux density of $\sim 2\,{\rm mJy}$ are probably
dominated by observational effects. At higher flux densities there are
intrinsic variations of polarization degree and angle within rather well
constrained ranges. Since the emission is most likely due to optically thin
synchrotron radiation, this preferred polarization angle we find is very likely
coupled to the intrinsic orientation of the Sgr A* system i.e. a disk or
jet/wind scenario associated with the super massive black hole. If they are
indeed linked to structural features of the source the data imply a rather
stable geometry and accretion process for the Sgr A* system.
