Community health centres in Tanzania have been evaluated for their efficiency gains over a specific period. A Bayesian hierarchical model was employed to analyse data from community health centres across different regions of Tanzania. The model accounts for both within-centre variability and centre differences, ensuring robust estimates of efficiency gains. The analysis revealed that the average efficiency gain in healthcare delivery varied by region, with some areas showing significant improvement (e.g., a 15% increase in patient satisfaction scores). The Bayesian hierarchical model provided nuanced insights into the performance variability among community health centres, highlighting disparities and potential for targeted interventions. Based on the findings, specific recommendations include focusing on improving infrastructure and training programmes to enhance efficiency in regions with lower efficiency gains. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.