Galactic outflows, driven by active galactic nuclei (AGN) and/or star formation, are a fundamental component of current galaxy evolution models within the Lambda Cold Dark Matter (ΛCDM) cosmology. These outflows are believed to significantly influence galaxy star formation efficiency, shape the stellar mass function, contribute to the chemical enrichment of the intergalactic medium and affect the dark matter distribution within galaxies. However, the comprehensive observational picture, especially regarding the dominant gas phase in these outflows, remains incomplete. The primary aim of this study is to statistically investigate the presence and properties of galactic-scale molecular gas outflows in local galaxies (z~0). Using CO (1-0) observations from the xCOLD GASS survey, we employed a combined stacking technique and the disc-decomposition line modeling method proposed by Concas et al. (2022) to search for non-circular motions indicative of outflows. Our findings reveal no statistically significant evidence for large-scale massive molecular outflows in the local universe. This result challenges the prevalent notion that massive molecular outflows are ubiquitous and suggests that their impact may be more nuanced than currently expected.