  The current view of galaxy formation holds that all massive galaxies harbor a
massive black hole at their center, but that these black holes are not always
in an actively accreting phase. X-ray emission is often used to identify
accreting sources, but for galaxies that are not harboring quasars
(low-luminosity active galaxies), the X-ray flux may be weak, or obscured by
dust. To aid in the understanding of weakly accreting black holes in the local
universe, a large sample of galaxies with X-ray detections is needed. We
cross-match the ROSAT All Sky Survey (RASS) with galaxies from the Sloan
Digital Sky Survey Data Release 4 (SDSS DR4) to create such a sample. Because
of the high SDSS source density and large RASS positional errors, the
cross-matched catalog is highly contaminated by random associations. We
investigate the overlap of these surveys and provide a statistical test of the
validity of RASS-SDSS galaxy cross-matches. SDSS quasars provide a test of our
cross-match validation scheme, as they have a very high fraction of true RASS
matches. We find that the number of true matches between the SDSS main galaxy
sample and the RASS is highly dependent on the optical spectral classification
of the galaxy; essentially no star-forming galaxies are detected, while more
than 0.6% of narrow-line Seyferts are detected in the RASS. Also, galaxies with
ambiguous optical classification have a surprisingly high RASS detection
fraction. This allows us to further constrain the SEDs of low-luminosity active
galaxies. Our technique is quite general, and can be applied to any
cross-matching between surveys with well-understood positional errors.
