The direct study of molecular gas in inner protoplanetary disks is complicated by uncertainties in the spatial distribution of the gas , the time-variability of the source , and the comparison of observations across a wide range of wavelengths . Some of these challenges can be mitigated with far-ultraviolet spectroscopy . Using new observations obtained with the Hubble Space Telescope -Cosmic Origins Spectrograph , we measure column densities and rovibrational temperatures for CO and H _ { 2 } observed on the line-of-sight through the AA Tauri circumstellar disk . CO A – X absorption bands are observed against the far-UV continuum . The CO absorption is characterized by log _ { 10 } ( N ( ^ { 12 } CO ) ) = 17.5 \pm 0.5 cm ^ { -2 } and T _ { rot } ( CO ) = 500 ^ { +500 } _ { -200 } K , although this rotational temperature may underestimate the local kinetic temperature of the CO-bearing gas . We also detect ^ { 13 } CO in absorption with an isotopic ratio of \sim 20 . We do not observe H _ { 2 } absorption against the continuum ; however , hot H _ { 2 } ( v > 0 ) is detected in absorption against the Ly \alpha emission line . We measure the column densities in eight individual rovibrational states , determining a total log _ { 10 } ( N ( H _ { 2 } ) ) = 17.9 ^ { +0.6 } _ { -0.3 } cm ^ { -2 } with a thermal temperature of T ( H _ { 2 } ) = 2500 ^ { +800 } _ { -700 } K. The high-temperature of the molecules , the relatively small H _ { 2 } column density , and the high-inclination of the AA Tauri disk suggest that the absorbing gas resides in an inner disk atmosphere . If the H _ { 2 } and CO are co-spatial within a molecular layer \sim 0.6 AU thick , this region is characterized by \langle n _ { H _ { 2 } } \rangle \sim 10 ^ { 5 } cm ^ { -3 } with an observed \langle CO/H _ { 2 } \rangle ratio of \sim 0.4 . We also find evidence for a departure from a purely thermal H _ { 2 } distribution , suggesting that excitation by continuum photons and H _ { 2 } formation may be altering the level populations in the molecular gas .