Context. Cosmic voids, distinguished by their low-density environment, provide a unique opportunity to explore the interplay between the cosmic environment and the processes of galaxy formation and evolution. Nevertheless, few data on the molecular gas have been obtained so far. Aims. In this paper, we continue the research performed in the CO-CAVITY pilot project to study the molecular gas content and properties in void galaxies in order to search for possible differences compared to galaxies that inhabit denser structures. Methods. We used the IRAM 30 m telescope to observe the CO(1–0) and CO(2–1) emission of 106 void galaxies selected from the CAVITY survey. Together with data from the literature, we obtained a sample of 200 void galaxies with CO data. We conducted a comprehensive comparison of the specific star formation rate (sSFR = SFR/M⋆), the molecular gas fraction (MH2/M⋆), and the star formation efficiency (SFE = SFR/MH2) between the void galaxies and a comparison sample of galaxies in filaments and walls selected from the xCOLD GASS survey. Results. We find no statistically significant difference between void galaxies and a comparison sample in the molecular gas fraction as a function of stellar mass for galaxies on the star-forming main sequence (SFMS). However, for void galaxies, the SFE is found to be constant across all stellar mass bins, while there is a decreasing trend with M⋆, for the comparison sample. Finally, we find some indications for a smaller dynamical range in the molecular gas fraction as a function of distance to the SFMS in void galaxies. Conclusions. Overall, we find that the molecular gas properties of void galaxies are not very different from those of denser environments. The physical origin of the most significant difference that we find – a constant SFE as a function of stellar mass in void galaxies – is unclear and further investigation and higher-resolution data are required to gain further insight.