Drowsiness at the wheel is one of the major contributing factors towards road accidents. Therefore, efforts have been made to detect driver drowsiness using electroencephalogram (EEG). The use of EEG as a possible driver drowsiness indicator is commonly accepted. However, in this paper, we have studied brain connectivity measure instead of the traditional spectral power measures. For this purpose, the EEG coherence analysis is performed to examine the functional connectivity between various brain regions during the transitional phase, i.e., from alert state to drowsy state. Data collection is performed in a simulator based environment. Twenty-two healthy subjects voluntarily participated in the study after providing their consent. All possible combinations of inter- and intra-hemispheric coherences are analyzed. Because of the unavailability of common gold standard, video recordings are captured during the experiment to mark the drowsy state. To verify the statistical significance of the proposed features, paired t-test is performed. The analysis revealed significant differences (p0.05) in inter- and intra-hemispheric coherences (brain connectivity analysis) between alert and drowsy state, which shows the potential of coherence analysis in detection drowsiness.