  We performed statistical and event studies of linear polarization in the
H$\alpha$ line during solar flares. The statistical study revealed that, among
71 H$\alpha$ flares analyzed, including 64 GOES flares, only one event shows
significant linear polarization signals. Such an infrequent occurrence of
significant linear polarization in solar flares is consistent with the result
by Bianda et al. (2005), who studied 30 flares and found no polarization
signals. In the event showing the significant polarization, the maximum degree
of linear polarization was 1.16$\pm$0.06\%, and the average direction of the
polarization deviated by -142.5$\pm$6.0 degrees from the solar north. The
observed polarization degrees and the directions are consistent with the
preceding reports (e.g. Henoux et al. 1990; Emslie et al. 2000; Hanaoka 2003).
These strong linear polarization signals did not appear at major flare ribbons,
nor did they correlate with either hard or soft X-ray emissions temporally or
spatially. Instead they appeared at a minor flare kernel, which corresponds to
one of the footpoints of a coronal loop. The active region caused coronal
dimming after the soft X-ray peak. The observed flare show no direct evidence
that the linear polarization is produced by high energy particles, which are
often considered to generate the polarization. On the other hand, our study
suggests the possibility that coronal mass ejections, which have been often
observed in flares showing linear polarization signals, play an important role
for exciting linear polarization at H$\alpha$ flare kernels.
