Parkinson's disease (PD) is a neurodegenerative disorder affecting millions of patients. Closed-Loop Deep Brain Stimulation (CL-DBS) is a therapy that can alleviate the symptoms of PD. The CL-DBS system consists of an electrode sending electrical stimulation signals to a specific region of the brain and a battery-powered stimulator implanted in the chest. The electrical stimuli in CL-DBS systems need to be adjusted in real-time in accordance with the state of PD symptoms. Therefore, fast and precise monitoring of PD symptoms is a critical function for CL-DBS systems. However, the current CL-DBS techniques suffer from high computational demands for real-time PD symptom monitoring, which are not feasible for implanted and wearable medical devices. In this paper, we present an energy-efficient neuromorphic PD symptom detector using memristive three-dimensional integrated circuits (3D-ICs). The excessive oscillation at beta frequencies (13-35 Hz) at the subthalamic nucleus (STN) is used as a biomarker of PD symptoms. Simulation results demonstrate that our neuromorphic PD detector, implemented with an 8-layer spiking Long Short-Term Memory (S-LSTM), excels in recognizing PD symptoms, achieving a training accuracy of 99.74% and a validation accuracy of 99.52% for a 75%-25% data split. Furthermore, we evaluated the improvement of our neuromorphic CL-DBS detector using NeuroSIM. The chip area, latency, energy, and power consumption of our CL-DBS detector were reduced by 47.4%, 66.63%, 65.6%, and 67.5%, respectively, for monolithic 3D-ICs. Similarly, for heterogeneous 3D-ICs, employing memristive synapses to replace traditional Static Random Access Memory (SRAM) resulted in reductions of 44.8%, 64.75%, 65.28%, and 67.7% in chip area, latency, and power usage. This study introduces a novel approach for PD symptom evaluation by directly utilizing spiking signals from neural activities in the time domain. This method significantly reduces the time and energy required for signal conversion compared to traditional frequency domain approaches. The study pioneers the use of neuromorphic computing and memristors in designing CL-DBS systems, surpassing SRAM-based designs in chip design area, latency, and energy efficiency. Lastly, the proposed neuromorphic PD detector demonstrates high resilience to timing variations in brain neural signals, as confirmed by robustness analysis.