  We build a large sample of Seyfert 2 galaxies (Sy2s) with both optical
spectropolarimetric and X-ray data available, in which 29 Sy2s with the
detection of polarized broad emission line (PBL) and 25 without. We find that
for luminous Sy2s with L_[OIII] > 10^41 erg/s, sources with PBL have smaller
X-ray absorption column density comparing with those without PBL (at 92.3%
confidence level): most of the Sy2s with N_H<10^23.8 cm^-2 show PBL (86%, 12
out 14), while the fraction is much smaller for sources with heavier
obscuration (54%, 15 out 28). The confidence level of the difference in
absorption bounces up to 99.1% while using the "T" ratio (F_2-10keV/F_[O III])
as an indicator. We rule out observation or selection bias as the origin for
the difference. Our results, for the first time with high statistical
confidence, show that, in additional to the nuclei activity, the nuclear
obscuration also plays an important role in the visibility of PBL in Sy2s.
These results can be interpreted in the framework of the unified model. We can
reach these results in the unified model if: a) the absorption column density
is higher at large inclinations and b) the scattering region is obscured at
large inclinations.
