We present low-resolution ($Rsim 90$) and medium-resolution ($Rsim 2500$) spectropolarimetry of Nova V475 Sct with the HBS instrument, mounted on the 0.91-m telescope at the Okayama Astrophysical Observatory, and with FOCAS, mounted on the 8.2-m Subaru telescope. We estimated the interstellar polarization toward the nova from the steady continuum polarization components and H$alpha$ line emission components. After subtracting the interstellar polarization component from the observations, we found that the H$alpha$ emission seen on 2003 October 7 was clearly polarized. In the polarized flux spectrum, the H$alpha$ emission had a distinct red wing extending to $sim +4900$ km s$^{-1}$ and a shoulder around $+3500$ km s$^{-1}$, showing a constant position angle of linear polarization $theta_{rm *}simeq 155arcdegpm 15arcdeg$. This suggests that the nova had an asymmetric outflow with a velocity of $v_{rm wind}simeq 3500$ km s$^{-1}$ or more, which is six times higher than the expansion velocity of the ionized shell at the same epoch. Such a high-velocity component has not previously been reported for a nova in the `moderately fast speed class. Our observations suggest the occurrence of violent mass-loss activity in the nova binary system even during the common-envelope phase. The position angle of the polarization in the H$alpha$ wing is in good agreement with that of the continuum polarization found on 2003 September 26 ($p_{rm *}simeq 0.4$--0.6 %), which disappeared within the following 2 d. The uniformity of the PA between the continuum polarization and the wing polarization on October 7 suggests that the axis of the circumstellar asymmetry remained nearly constant during the period of our observations.
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