Electroencephalography (EEG) signals may provide abundant information reflecting the developmental changes in brain status. It usually takes a long time to finally judge whether a brain is dead, so an effective pre-test of brain states method is needed. In this paper, we present a hybrid processing pipeline to differentiate brain death and coma patients based on canonical correlation analysis (CCA) of power spectral density, complexity features, and feature fusion for group analysis. In addition, time-varying power spectrum and complexity were observed based on the analysis of individual patients, which can be used to monitor the change of brain status over time. Results showed three major differences between brain death and coma groups of EEG signal: slowing, increased complexity, and the improvement on classification accuracy with feature fusion. To the best of our knowledge, this is the first scheme for joint general analysis and time-varying state monitoring. Delta-band relative power spectrum density and permutation entropy could effectively be regarded as potential features of discrimination analysis on brain death and coma patients.