Community health centres (CHCs) in South Africa play a crucial role in delivering primary healthcare services to underserved populations. However, their operational efficiency varies significantly. A two-stage least squares (2SLS) regression model was employed to estimate efficiency gains in South African CHCs. The study utilised a dataset comprising 10 years of quarterly operational data from 50 randomly selected CHCs across the country. The analysis revealed that average efficiency scores for CHCs were above 80%, indicating substantial room for improvement through targeted interventions and resource reallocation. This study provides a robust methodology to assess CHC efficiency, which can inform policy decisions aimed at enhancing service delivery quality in South Africa. Strategic investments should be directed towards areas with the lowest efficiency scores identified. Additionally, regular performance monitoring and periodic capacity-building initiatives are recommended. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.