Inter-hemispheric sleep EEG coherence is studied in 10 subjects with psycho physiological insomnia, in 10 with paradoxical insomnia, and in 10 matched controls through different states of the sleep/wakefulness cycle. Inter hemispheric EEG coherence between central electrode pairs are compared to each other within these groups. A linear measure called as Coherence Function (CF) and a nonlinear measure called as Mutual Information (MI) are performed by using the Information Theory Toolbox in the present sleep EEG synchronization study. Regarding as tests, for all-night EEG recordings of participants, both measures indicate higher degree of EEG coherence for insomnia than for controls. The results further validate inter-hemispheric CF as a sign of activity in insomnia where the EEG series from stage2, REM sleep and the eyes closed waking state. In particular, the CF is found to be more useful tool than the MI for detection of insomnia when the power spectral density estimations of sleep stages are provided by the Burg Method. In conclusion, the CF provides insights into functional connectivity of brain regions during sleep. Since the CF has a characteristic shape for sleep states, it can be proposed to identify the degree of EEG complexity depending on sleep disorders.