  Carbon monoxide (CO) is the most commonly used tracer of molecular gas in the
inner regions of protoplanetary disks. CO can be used to constrain the
excitation and structure of the circumstellar environment. Absorption line
spectroscopy provides an accurate assessment of a single line-of-sight through
the protoplanetary disk system, giving more straightforward estimates of column
densities and temperatures than CO and molecular hydrogen emission line
studies. We analyze new observations of ultraviolet CO absorption from the
Hubble Space Telescope along the sightlines to six classical T Tauri stars. Gas
velocities consistent with the stellar velocities, combined with the
moderate-to-high disk inclinations, argue against the absorbing CO gas
originating in a fast-moving disk wind. We conclude that the far-ultraviolet
observations provide a direct measure of the disk atmosphere or possibly a slow
disk wind. The CO absorption lines are reproduced by model spectra with column
densities in the range N(^{12}CO) ~ 10^{16} - 10^{18} cm^{-2} and N(^{13}CO) ~
10^{15} - 10^{17} cm^{-2}, rotational temperatures T_{rot}(CO) ~ 300 - 700 K,
and Doppler b-values, b ~ 0.5 - 1.5 km s^{-1}. We use these results to
constrain the line-of-sight density of the warm molecular gas (n_{CO} ~ 70 -
4000 cm^{-3}) and put these observations in context with protoplanetary disk
models.
