District hospitals in Uganda play a critical role in primary healthcare delivery, yet their operational efficiency varies widely, necessitating methodological evaluation to optimise resources and improve service quality. A quasi-experimental approach was employed with a structural equation modelling (SEM) framework to estimate efficiency gains. The study utilised data from 10 randomly selected districts over two years, including inputs and outputs of services provided in the hospitals. The analysis revealed significant variation in operational efficiency among districts, with some achieving efficiencies up to 20% above the national average. These findings suggest potential for targeted interventions to enhance service delivery. This study provides a robust methodological framework for evaluating district hospital systems and offers insights into areas needing improvement to meet healthcare standards. Policy recommendations include prioritising resource allocation in districts with lower efficiency scores, implementing training programmes for staff, and promoting health education campaigns. District Hospitals, Efficiency Evaluation, Quasi-Experimental Design, Structural Equation Modelling Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.