The central sulcus is probably one of the most studied folds in the human brain, owing to its clear relationship with primary sensory-motor functional areas. However, due to the difficulty of estimating the trajectories of the U-shape fibres from diffusion MRI, the short structural connectivity of this sulcus remains relatively unknown. In this context, we studied the spatial organization of these U-shape fibres along the central sulcus. Based on high quality diffusion MRI data of 100 right-handed subjects and state-of-the-art pre-processing pipeline, we first define a connectivity space that provides a comprehensive and continuous description of the short-range anatomical connectivity around the central sulcus at both the individual and group levels. We then infer the presence of five major U-shape fibre bundles at the group level in both hemispheres by applying unsupervised clustering in the connectivity space. We propose a quantitative investigation of their position and number of streamlines as a function of hemisphere, sex and functional scores such as handedness and manual dexterity. Main findings of this study are twofold: a description of U-shape short-range connectivity along the central sulcus at group level and the evidence of a significant relationship between the position of three hand related U-shape fibre bundles and the handedness score of subjects.