Background and objectives: Dynamic handwriting analysis, due to its non-invasive and readily accessible nature, has recently emerged as a vital adjunctive method for the early diagnosis of Parkinson's disease. In this study, we design a compact and efficient network architecture to analyse the distinctive handwriting patterns of patients' dynamic handwriting signals, thereby providing an objective identification for the Parkinson's disease diagnosis. Methods: The proposed network is based on a hybrid deep learning approach that fully leverages the advantages of both long short-term memory (LSTM) and convolutional neural networks (CNNs). Specifically, the LSTM block is adopted to extract the time-varying features, while the CNN-based block is implemented using one-dimensional convolution for low computational cost. Moreover, the hybrid model architecture is continuously refined under ablation studies for superior performance. Finally, we evaluate the proposed method with its generalization under a five-fold cross-validation, which validates its efficiency and robustness. Results: The proposed network demonstrates its versatility by achieving impressive classification accuracies on both our new DraWritePD dataset ($96.2\%$) and the well-established PaHaW dataset ($90.7\%$). Moreover, the network architecture also stands out for its excellent lightweight design, occupying a mere $0.084$M of parameters, with a total of only $0.59$M floating-point operations. It also exhibits near real-time CPU inference performance, with inference times ranging from $0.106$ to $0.220$s. Conclusions: We present a series of experiments with extensive analysis, which systematically demonstrate the effectiveness and efficiency of the proposed hybrid neural network in extracting distinctive handwriting patterns for precise diagnosis of Parkinson's disease.