Brain–computer interface technologies, as a type of human-computer interaction, provide a control ability on machines and intelligent systems via human brain functions without needing physical contact. Moreover, it has a considerable contribution to the detection of cognitive state changes, which gives a clue for neurodegenerative diseases, including Parkinson’s disease (PD), in recent years. Although various studies implemented different machine learning models with several EEG features to detect PD and receive remarkable performances, there is a lack of knowledge on how brain connectivity during a cognitive task contributes to the differentiation of PD, even being under medication. To fill this gap, this study used three ensemble classifiers, which were fed by functional connectivity through cognitive response coherence (CRC) with varying selected features in different frequency bands upon application of the 3-Stimulation auditory oddball paradigm to differentiate PD medication ON and OFF and healthy controls (HC). The results revealed that the most remarkable performances were exhibited in slow frequency bands (delta and theta) in comparison to high frequency and wide range bands, especially in terms of target sounds. Moreover, in the delta band, target CRC distinguishes all groups from each other with accuracy rates of 80% for HC vs PD-OFF, 80% for HC vs PD-ON, and 81% for PD-ON vs PD-OFF. In the theta band, again target sounds were the most distinctive stimuli to classify HCxPD-OFF (80% accuracy), HCxPD-ON (80.5% accuracy) with quite good performances, and PD-ONxPD-OFF (76% accuracy) with acceptable performance. Besides, this study achieved a state-of-the-art performance with an accuracy of 87.5% in classifying PD-ONxPD-OFF via CRC of standard sounds in the delta band. Overall, the findings revealed that brain connectivity contributes to identifying PD and HC as well as the medication state of PD, especially in the slow frequency bands.