Fairness in clinical decision-making is a critical element of health equity, but assessing fairness of clinical decisions from observational data is challenging. Recently, many fairness notions have been proposed to quantify fairness in decision-making, among which causality-based fairness notions have gained increasing attention due to its potential in adjusting for confounding and reasoning about bias. However, causal fairness notions remain under-explored in the context of clinical decision-making with large-scale healthcare data. In this work, we propose a Bayesian causal inference approach for assessing a causal fairness notion called principal fairness in clinical settings. We demonstrate our approach using both simulated data and electronic health records (EHR) data.