Parkinson’s disease (PD) is a neurodegenerative disorder characterized by the gradual deterioration of motor function, affecting speech, writing, muscle control, and mobility. The existing studies have not utilized both the electroencephalography (EEG) signals and online handwritten tasks together to diagnose PD. The studies have also not explored the EEG signals collected from specific brain regions like the substansia niagra (SN) and ventral tegmental area (VTA), crucial for dopamine production linked to PD. This article proposes a multi-modal PD diagnosis system from EEG signals (collected from SN and VTA regions of the brain), collected during performing online handwritten tasks, using grey wolf optimization (GWO) algorithm. Mel-frequency cepstral coefficients (MFCC) features have been generated from the EEG signals and optimized by the GWO algorithm. The classification (diagnosis) experiments on the optimal number of feature values, obtained from GWO algorithm, have been carried out using bidirectional long short-term memory (BLSTM) variant of recurrent neural network (RNN). The classification experiments have also been conducted using support vector machine (SVM), bagged random forest (BRF), and long short-term memory (LSTM) variant of RNN classifier to have a performance comparison with the proposed method. The effectiveness of the introduced PD diagnosis system has been analyzed on a self-generated dataset named EEG signal based on online handwriting (ESOH). A maximum classification accuracy of 99.30% has been achieved from the proposed PD diagnosis system. The experimental outcomes illustrate that the introduced PD diagnosis system outperforms the state-of-the-art PD diagnosis systems relying on the EEG signals for diagnosing the PD.