We investigate the emission-line properties of galaxies with red rest-frame colors (compared to the g - r color bimodality) using spectra from SDSS DR4. Emission lines are detected in more than half of the red galaxies. We focus on the relationship between two emission lines commonly used as star formation rate indicators: Hα and [O II] λ3727. There is a strong bimodality in [O II]/Hα ratio in the SDSS sample that closely corresponds to the bimodality in rest-frame color. Nearly all of the line-emitting red galaxies have line ratios typical of various types of AGNs—most commonly LINERs, a small fraction of transition objects, and, more rarely, Seyferts. Only ~6% of red galaxies display star-forming line ratios. A straight line in the [O II]-Hα EW diagram separates LINER-like galaxies from other categories. Quiescent galaxies with no detectable emission lines and LINER-like galaxies combine to form a single, tight red sequence in color-magnitude-concentration space. [O II] EWs in LINER- and AGN-like galaxies can be as large as those in star-forming galaxies. Thus, unless objects with AGN/LINER-like line ratios are excluded, [O II] emission cannot be used directly as a proxy for star formation rate; this is a particular issue for red galaxies. Lack of [O II] emission is generally used to indicate a lack of star formation when poststarburst galaxies are selected at high redshift. Our results imply, however, that these samples have been cut on AGN properties, as well as star formation, and therefore may provide seriously incomplete sets of poststarburst galaxies. Furthermore, poststarburst galaxies identified in SDSS by requiring minimal Hα EW generally exhibit weak but nonzero line emission with ratios typical of AGNs; few of them show residual star formation. This suggests that most poststarburst galaxies may harbor AGNs/LINERs.
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