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 ( H _ { 2 } ) 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 ) \sim 10 ^ { 16 } -10 ^ { 18 } cm ^ { -2 } and N ( ^ { 13 } CO ) \sim 10 ^ { 15 } -10 ^ { 17 } cm ^ { -2 } , rotational temperatures T _ { rot } ( CO ) \sim 300 – 700 K , and Doppler b -values , b \sim 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 } \sim 70 - 4000 cm ^ { -3 } ) and put these observations in context with protoplanetary disk models .