Hosting nearly eighty percent of all human neurons, the cerebellum is functionally connected to large regions of the brain. Accumulating data suggest that some cerebellar resting-state alterations may constitute a key candidate mechanism for depressive psychopathology. While there is some evidence linking cerebellar function and depression, two topics remain largely unexplored. First, the genetic or environmental roots of this putative association have not been elicited. Secondly, while different mathematical representations of resting-state fMRI patterns can embed diverse information of relevance for health and disease, many of them have not been studied in detail regarding the cerebellum and depression. Here, high-resolution fMRI scans were examined to estimate functional connectivity patterns across twenty-six cerebellar regions in a sample of 48 identical twins (24 pairs) informative for depression liability. A network-based statistic approach was employed to analyze cerebellar functional networks built using three methods: the conventional approach of filtered BOLD fMRI time-series, and two analytic components of this oscillatory activity (amplitude envelope and instantaneous phase). The findings indicate that some environmental factors may lead to depression vulnerability through alterations of the neural oscillatory activity of the cerebellum during resting-state. These effects may be observed particularly when exploring the amplitude envelope of fMRI oscillations.