  We present seven epochs of spectropolarimetry of the Type IIb supernova (SN)
2011dh in M51, spanning 86 days of its evolution. The first epoch was obtained
9 days after the explosion, when the photosphere was still in the depleted
hydrogen layer of the stripped-envelope progenitor. Continuum polarization is
securely detected at the level of P~0.5% through day 14 and appears to diminish
by day 30, which is different from the prevailing trends suggested by studies
of other core-collapse SNe. Time-variable modulations in P and position angle
are detected across P-Cygni line features. H-alpha and HeI polarization peak
after 30 days and exhibit position angles roughly aligned with the earlier
continuum, while OI and CaII appear to be geometrically distinct. We discuss
several possibilities to explain the evolution of the continuum and line
polarization, including the potential effects of a tidally deformed progenitor
star, aspherical radioactive heating by fast-rising plumes of Ni-56 from the
core, oblique shock breakout, or scattering by circumstellar material. While
these possibilities are plausible and guided by theoretical expectations, they
are not unique solutions to the data. The construction of more detailed
hydrodynamic and radiative-transfer models that incorporate complex aspherical
geometries will be required to further elucidate the nature of the polarized
radiation from SN 2011dh and other Type IIb supernovae.
