We present spectropolarimetric observations of the nuclei of four Seyfert 2 galaxies, Mrk 477 Mrk 1210, NGC 7212, and Was 49b. The data, covering the spectral range 4600-7400 angstrom at moderate resolution, were obtained with the CCD spectrograph/polarimeter attached to the 3 m Shane telescope at Lick Observatory. They show clear evidence for broad components of Halpha and Hbeta emission lines in the polarized flux spectra of these objects, similar to those observed in NGC 1068 and four other previously known obscured Seyfert 1 galaxies reported by Miller & Goodrich. Based on the wavelength behavior of the continuum polarization and the relatively low polarization of the forbidden lines, it seems most likely that the polarization of the four objects in the present study arises from scattering by electrons and/or dust clouds outside the obscured broad-line region but within the narrow-line region. The detection of the hidden nuclei of Seyfert 1 type within these Seyfert 2 galaxies significantly increases the total number of such objects known and strengthens the support for the obscuration/reflection model of the unified Seyfert schemes.