Assessing the efficiency of public expenditure and identifying the origins of inefficiency is imperative for any government to design effective policy measures. This study aims to decompose the efficiency of health and education expenditure of major Indian states as a two-stage process in which the first stage is infrastructure development and the second is service delivery. Using a two-stage relational Data Envelopment Analysis of (Kao and Hwang, European Journal of Operational Research 185:418–429, 2008) for the year 2019–2020, the empirical findings from this study suggest a significant variation in efficiency across the states in these two stages. Further, it also identifies that the governance of a state matters only in the infrastructure stage and not in the service delivery stage. The results from this study will help the states understand the stage where they have deficiencies and design their policy for improvement.