We obtained CO(2-1) observations of seven GRB hosts with the APEX and IRAM 30m telescopes. We analysed these data together with all other hosts with previous CO observations. We obtained detections for 3 GRB hosts (980425, 080207, and 111005A) and upper limits for the remaining 4 (031203, 060505, 060814, and 100316D). In our entire sample of 12 CO-observed GRB hosts, 3 are clearly deficient in molecular gas, even taking into account their metallicity (980425, 060814, and 080517). Four others are close to the best-fit line for other star-forming galaxies on the SFR-MH2 plot (051022, 060505, 080207, and 100316D). One host is clearly molecule rich (111005A). Finally, the data for 4 GRB hosts are not deep enough to judge whether they are molecule deficient (000418, 030329, 031203, and 090423). The median value of the molecular gas depletion time, MH2/SFR, of GRB hosts is ~0.3 dex below that of other star-forming galaxies, but this result has low statistical significance. A Kolmogorov-Smirnov test performed on MH2/SFR shows an only ~2sigma difference between GRB hosts and other galaxies. This difference can partly be explained by metallicity effects, since the significance decreases to ~1sigma for MH2/SFR versus~metallicity. We found that any molecular gas deficiency of GRB hosts has low statistical significance and that it can be attributed to their lower metallicities; and thus the sample of GRB hosts has molecular properties that are consistent with those of other galaxies, and they can be treated as representative star-forming galaxies. Given the concentration of atomic gas recently found close to GRB and supernova sites, indicating recent gas inflow, our results about the weak molecular deficiency imply that such an inflow does not enhance the SFRs significantly, or that atomic gas converts efficiently into the molecular phase, which fuels star formation.
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