  The 18806 ROSAT All Sky Survey Bright Source Catalog (RASS/BSC) X-ray sources
are quantitatively cross-associated with near-infrared (NIR) sources from the
Two Micron All Sky Survey Point Source Catalog (2MASS/PSC). An association
catalog is presented, listing the most likely counterpart for each RASS/BSC
source, the probability Pid that the NIR source and X-ray source are uniquely
associated, and the probability Pnoid that none of the 2MASS/PSC sources are
associated with the X-ray source. The catalog includes 3853 high quality
(Pid>0.98) X-ray--NIR matches, 2280 medium quality (0.98>Pid>0.9) matches, and
4153 low quality (0.9>Pid>0.5) matches. Of the high quality matches, 1418 are
associations that are not listed in the SIMBAD database, and for which no high
quality match with a USNO-A2 optical source was presented for the RASS/BSC
source in previous work. The present work offers a significant number of new
associations with RASS/BSC objects that will require optical/NIR spectroscopy
for classification. For example, of the 6133 Pid>0.9 2MASS/PSC counterparts
presented in the association catalog, 2411 have no classification listed in the
SIMBAD database. These 2MASS/PSC sources will likely include scientifically
useful examples of known source classes of X-ray emitters (white dwarfs,
coronally active stars, active galactic nuclei), but may also contain
previously unknown source classes. It is determined that all coronally active
stars in the RASS/BSC should have a counterpart in the 2MASS/PSC, and that the
unique association of these RASS/BSC sources with their NIR counterparts thus
is confusion limited.
