The aim of this work was to verify the technical efficiency (i.e., if it is possible use the minimum quantity of inputs required to produce the desired output quantity, given the available technology) of the Brazilian states in relation to public expenditure on health and education after the implementation of the Fiscal Responsibility Law (LRF). For this, a parametric model of stochastic frontier estimation of production and the decomposition of the variation of technical efficiency (VTE) and technological variation by means of the Malmquist index for the Brazilian states were used. Input indicators (expenditure on health and education per capita) were obtained from the National Treasury Secretariat of the Ministry of Finance (Secretaria do Tesouro Nacional/Ministério da Fazenda). Data for output and outcomes in the health area were obtained from Datasus. The data for output and outcomes in the education area were obtained from Ipeadata. The data period is from 2001 to 2012. The results show that, in relation to education expenditures, there is a positive and statistically significant relationship between spending on education per capita and approval rate in secondary education. Regarding the health area, the results show that health expenditures per capita presented a statistically significant and negative relationship with the infant mortality rate in the respective Brazilian states. In relation to the decomposition of the VTE and technological variation through the Malmquist index, all states, both in education and in health, were below the technical efficiency frontier. It should be noted that most of the analyses already carried out of this kind in Brazil focus on the technical efficiency of only the health sector or the education sector separately, while this present work aims to deal with the efficiency of the two sectors.