The Connectome File Format is used by the Connectome Viewer to organize multi-modal datasets for a single subject or a study. The Connectome File Format Version 2.0 is released together with the Connectome File Format Library (cfflib), enabling creation, manipulation and storage of its contained data.
To get started, you can look into the documentation for the cfflib or explore the connectome file data repository cffdata.
The library and format heavily depends on neuroimaging data format reader/writers implemented in Nibabel.