Context. Long gamma-ray bursts (GRBs) can potentially be used as a tool to study star formation and recent gas accretion onto galaxies. However, the information about gas properties of GRB hosts is scarce. In particular, very few carbon monoxide (CO) line detections of individual GRB hosts have been reported. It has also been suggested that GRB hosts have lower molecular gas masses than expected from their star formation rates (SFRs). Aims. The objectives of this paper are to analyse molecular gas properties of the first substantial sample of GRB hosts and test whether they are deficient in molecular gas. Methods. We obtained CO(2-1) observations of seven GRB hosts with the APEX and IRAM 30 m telescopes. We analysed these data together with all other hosts with previous CO observations. From these observations we calculated the molecular gas masses of these galaxies and compared them with the expected values based on their SFRs and metallicities. Reults. 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-M-H2 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, M-H2/SFR, of GRB hosts is similar to 0.3 dex below that of other star-forming galaxies, but this result has low statistical significance. A Kolmogorov-Smirnov test performed on M-H2/SFR shows an only similar to 2 sigma difference between GRB hosts and other galaxies. This difference can partly be explained by metallicity effects, since the significance decreases to similar to 1 sigma for M-H2/SFR versus metallicity. Conclusions. 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. However, the molecular gas deficiency can be strong for GRB hosts if they exhibit higher excitations and/or a lower CO-to-H-2 conversion factor than we assume, which would lead to lower molecular gas masses than we derive. 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. Only if the analysis of a larger GRB host sample reveals molecular deficiency (especially close to the GRB position) would this support the hypothesis of star formation that is directly fuelled by atomic gas.