This study highlights the potential of fine-tuned ChatGPT (GPT-3.5) for automatically scoring student written constructed responses using example assessment tasks in science education. Recent studies on OpenAI's generative model GPT-3.5 proved its superiority in predicting the natural language with high accuracy and human-like responses. GPT-3.5 has been trained over enormous online language materials such as journals and Wikipedia; therefore, more than direct usage of pre-trained GPT-3.5 is required for automatic scoring as students utilize a different language than trained material. These imply that a domain-specific model, fine-tuned over data for specific tasks, can enhance model performance. In this study, we fine-tuned GPT-3.5 on six assessment tasks with a diverse dataset of middle-school and high-school student responses and expert scoring. The six tasks comprise two multi-label and four multi-class assessment tasks. We compare the performance of fine-tuned GPT-3.5 with the fine-tuned state-of-the-art Google's generated language model, BERT. The results show that in-domain training corpora constructed from science questions and responses for BERT achieved average accuracy = 0.838, SD = 0.069. GPT-3.5 shows a remarkable average increase (9.1%) in automatic scoring accuracy (mean = 9.15, SD = 0.042) for the six tasks, p =0.001 < 0.05. Specifically, for multi-label tasks (item 1 with 5 labels; item 2 with 10 labels), GPT-3.5 achieved significantly higher scoring accuracy than BERT across all the labels, with the second item achieving a 7.1% increase. The average scoring increase for the four multi-class items for GPT-3.5 was 10.6% compared to BERT. Our study confirmed the effectiveness of fine-tuned GPT-3.5 for automatic scoring of student responses on domain-specific data in education with high accuracy. We have released fine-tuned models for public use and community engagement.