Fresh gully-like features on Mars strongly suggest that fluid flowed on the surface in the recent past. Here we consider the possibility that CO2 vapor-supported flows formed the gullies. We find that neither condensed CO2 nor CO2 clathrate hydrate are likely to accumulate in significant quantities in the Martian crust. In addition, if condensed CO2 were present under lithostatic pressures, exposure to the atmosphere would produce features analogous to terrestrial pyroclastic flows, not surface runoff. Finally, the source volume of CO2 required to support a flow excludes clustered or episodic gully formation. Therefore, we conclude that CO2 cannot have formed the gullies. In light of these results, liquid water flow remains the preferred formation mechanism for the recent surface runoff features.