We present high resolution 4.7 \hbox { $ \mu$m } CO fundamental spectroscopy of V836 Tau , a young star with properties that are between those of classical and weak T Tauri stars and which may be dissipating its circumstellar disk . We find that the CO line profiles of V836 Tau are unusual in that they are markedly double-peaked , even after correcting for stellar photospheric absorption in the spectrum . This suggests that the CO emission arises from a restricted range of disk radii ( < 0.5 AU ) , in contrast to the situation for most classical T Tauri stars where the CO emission extends out to much larger radii ( \sim 1 - 2 AU ) . We discuss whether the outer radius of the emission in V836 Tau results from the physical truncation of the disk or an excitation effect . We also explore how either of these hypotheses may bear on our understanding of disk dissipation in this system .