Parkinson’s disease (PD) is the most common degenerative movement disorder and a progressive nervous system disorder. It affects body movement, memory, speaking and daily mental and physical activities, being directly connected to the dopaminergic loss. The EEG signal can be modulated under the effect of neurotransmitters, e.g., using dopamine (L-dopa), the alpha and beta frequencies (the characteristic of normal EEG activity at rest) increase, and reduce delta-theta activities. Joint EEG and EMG signals from 22 patients (16 men and 6 women of 62 years on average) have been acquired on several mental tasks. These patients were diagnosed with PD according to the UK PD Society Brain Bank diagnostic criteria, while the EEG recording was performed according to the International 10–20 System. Nowadays, there is no screening test for early detection of PD. Symptoms become increasingly visible as the disease progresses. The Hurst coefficient is one of the indicators that could be used for the characterization of EEG signals, as these signals may be seen as processes with extended memory. The results obtained for the patients with PD, PD and Dementia, PD and diabetes present lower Hurst coefficient values for the delta rhythm. In the case of healthy subjects a decrease of Hurst coefficient values for this rhythm was not observed. In conclusion, the Hurst coefficient applied to EEG signals can be a good marker for the early diagnosis of PD, and maybe other neurodegenerative diseases.