Large language models (LLM) have been successful in several natural language understanding tasks and could be relevant for natural language processing (NLP)-based mental health application research. In this work, we report the performance of LLM-based ChatGPT (with gpt-3.5-turbo backend) in three text-based mental health classification tasks: stress detection (2-class classification), depression detection (2-class classification), and suicidality detection (5-class classification). We obtained annotated social media posts for the three classification tasks from public datasets. Then ChatGPT API classified the social media posts with an input prompt for classification. We obtained F1 scores of 0.73, 0.86, and 0.37 for stress detection, depression detection, and suicidality detection, respectively. A baseline model that always predicted the dominant class resulted in F1 scores of 0.35, 0.60, and 0.19. The zero-shot classification accuracy obtained with ChatGPT indicates a potential use of language models for mental health classification tasks.