The thesis aimed to analyze the efficiency of public security expenditures in controlling the crime of death due to external causes (homicide) and socioeconomic variables in the municipalities belonging to the Federated States of the Legal Amazon from 2002 to 2015. The methodology used consisted in estimating a technical efficiency score calculated by municipality and with this it stratified by layers of isoefficiency the obtained results, delimited in this way: 0,01 and 0,25 (low efficiency), 0,25 and 0,50 ( (efficiency), 0.50 and 0.75 (average efficiency), and 0.75 and 1.00 (high efficiency), according to the Data Envelopment Analysis (DEA) model. The hypotheses tested were as follows: Hypothesis 01: The evolution of the overall total efficiency score (eftg), for the control of death from external causes (homicide), presents different quantitative and qualitative magnitudes correlated with the socioeconomic nature of the municipalities belonging to the Legal Amazon in the period from 2002 to 2015, being largely classified as Low efficiency. Hypothesis 02: The evolution of the efficiency score by population size, for the control of death from external causes (homicide), presents different quantitative and qualitative magnitudes correlated to the population nature of the municipalities belonging to the Legal Amazon from 2002 to 2015, being large part classified as High efficiency. The results obtained by empirical comparison of the descriptive mean indicate that the efficiency estimation for the control of the crime of death due to external causes (homicide) is delimited by socioeconomic, institutional and population factors, among the municipalities belonging to the Legal Amazon in the period from 2002 to 2015.
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