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 [ ] , 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 . \citealp heno90b , emsl00 , hana03 ) .
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 .