(Abridged) We describe a sample of low-mass Seyfert 2 galaxies selected from the Sloan Digital Sky Survey, having a median absolute magnitude of M_g = -19.0 mag. These galaxies are Type 2 counterparts to the Seyfert 1 galaxies with intermediate-mass black holes identified by Greene & Ho (2004). Spectra obtained with the Echellette Spectrograph and Imager at the Keck Observatory are used to determine the central stellar velocity dispersions and to examine the emission-line properties. Overall, the stellar velocity dispersions are low (40-90 km/s), and we find 12 objects having sigma < 60 km/s, a range where very few Seyfert 2 galaxies were previously known. The sample follows the correlation between stellar velocity dispersion and FWHM([OIII]) seen in more massive Seyfert galaxies, indicating that the narrow-line FWHM values are largely determined by virial motion of gas in the central regions of the host galaxies. Using estimates of the black hole masses and AGN bolometric luminosities, we find that these galaxies are typically radiating at a high fraction of their Eddington rate, with a median L_bol/L_Edd = 0.4. We identify one galaxy, SDSS J110912.40+612346.7, as a Type 2 analog of the nearby dwarf Seyfert 1 galaxy NGC 4395, with a nearly identical narrow-line spectrum and a dwarf spiral host of only M_g = -16.8 mag. Forthcoming observations of this sample, including X-ray and mid-infrared spectroscopy, can provide new tests of the obscuring torus model for active galaxies at low luminosities.
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