Document classification is a widely used approach for analysing mental healthcare texts. This systematic literature review focuses on document classification in healthcare notes obtained from electronic health records within mental health care. We observe that the last decade has been characterized by a shift from rule-based methods to machine-learning methods. However, while the shift towards machine-learning methods is evident, there is currently no systematic comparison of both methods for document classification in applications in mental healthcare. In this work, we perform a systematic literature review to assess how these methods compare in terms of performance, which are the specific applications and tasks, and how the approaches have developed throughout time. We find that for most of the last decade, rule-based methods have performed better than machine-learning methods. However, recent developments towards healthcare data availability in combination with self-learning neural networks and transformer-based large language models result in higher performance.