  We present near-infrared K-band slit spectra of the nuclei of 25 Seyfert 2
galaxies in the CfA and 12 micron samples. The strength of the CO absorption
features at 2.3-2.4 micron produced by stars is measured in terms of a
spectroscopic CO index. A clear anti-correlation between the observed CO index
and the nuclear K-L color is present, suggesting that a featureless hot dust
continuum heated by an AGN contributes significantly to the observed K-band
fluxes in the nuclei of Seyfert 2 galaxies. After correction for this AGN
contribution, we estimate nuclear stellar K-band luminosities for all sources,
and CO indices for sources with modestly large observed CO indices. The
corrected CO indices for 10 (=40%) Seyfert 2 nuclei are found to be as high as
those observed in star-forming or elliptical (=spheroidal) galaxies. We combine
the K-band data with measurements of the L-band 3.3 micron polycyclic aromatic
hydrocarbon (PAH) emission feature, another powerful indicator for
star-formation, and find that the 3.3 micron PAH to K-band stellar luminosity
ratios are substantially smaller than those of starburst galaxies. Our results
suggest that the 3.3 micron PAH emission originates in the putative nuclear
starbursts in the dusty tori surrounding the AGNs, because of its high surface
brightness, whereas the K-band CO absorption features detected at the nuclei
are dominated by old bulge (=spheroid) stars, and thus may not be a powerful
indicator for the nuclear starbursts. We see no clear difference in the
strength of the CO absorption and PAH emission features between the CfA and 12
micron Seyfert 2s.
