Recent studies have demonstrated an overlap between the neural substrate of resting-state activity and self-related processing in the cortical midline structures (CMS). However, the neural and psychological mechanisms mediating this so-called “rest-self overlap” remain unclear. To investigate the neural mechanisms, we estimated the temporal structure of spontaneous/resting-state activity, e.g. its long-range temporal correlations or self-affinity across time as indexed by the power-law exponent (PLE). The PLE was obtained in resting-state activity in the medial prefrontal cortex (MPFC) and the posterior cingulate cortex (PCC) in 47 healthy subjects by functional magnetic resonance imaging (fMRI). We performed correlation analyses of the PLE and Revised Self-Consciousness Scale (SCSR) scores, which enabled us to access different dimensions of self-consciousness and specified rest-self overlap in a psychological regard. The PLE in the MPFC's resting-state activity correlated with private self-consciousness scores from the SCSR. Conversely, we found no correlation between the PLE and the other subscales of the SCSR (public, social) or between other resting-state measures, including functional connectivity, and the SCSR subscales. This is the first evidence for the association between the scale-free dynamics of resting-state activity in the CMS and the private dimension of self-consciousness. This finding implies the relationship of especially the private dimension of self with the temporal structure of resting-state activity.