  We present imaging circular polarimetry and near-infrared photometry of the
suspected ultra-short period white-dwarf binary RX J0806.3+1527 obtained with
the ESO VLT and discuss the implications for a possible magnetic nature of the
white dwarf accretor and the constraints derived for the nature of the donor
star. Our V-filter data show marginally significant circular polarization with
a modulation amplitude of ~0.5% typical for cyclotron emission from an
accretion column in a magnetic field of order 10 MG and not compatible with a
direct-impact accretor model. The optical to near-infrared flux distribution is
well described by a single blackbody with temperature kT_bb = 35000 K and
excludes a main-sequence stellar donor unless the binary is located several
scale heights above the galactic disk population.
