Background: The benchmarking literature has made important advances and offers many different population health indicators that can be used to compare state health systems. However, there is still a need for qualitative, complexity-oriented approaches that allow policy-makers to develop explanatory 'policy stories' from combining such indicators that are useful to policy solutions. Methods: A new qualitative method from the social sciences based on Boolean approaches, called Qualitative Comparative Analysis (QCA), was piloted in a 'real world' policy consultancy to combine Australian state-level indicators of community and health system inputs, interventions, and population health outcomes. Analyses were provided for state inputs and outcomes in a specific area of chronic disease (mental health), along with state profiling for differences in risky health-related behaviours. Results: The QCA method suggested that the state of Tasmania may resemble South Australia in terms of having lower community inputs, as well as higher levels of mental health system inputs and interventions (such as prescriptions), than other states with the outcome of higher self-reported psychological distress. Theoretically, employment levels explained state-level differences in self-reported psychological distress. In terms of risky health-related behaviours, the QCA suggested that Tasmania leads other states in both socio-economic challenges and risky health behaviours. Theoretically, smoking explained state-level differences in self-assessed health. Conclusions: The QCA method has its weaknesses, but in this study, it allowed for the development of policy stories based on systematic comparisons of different states. It also suggested theoretically plausible explanations for differences in state-level outcomes.