High accident rates are observed on Brazilian roads. Among other factors, the number of accidents is highly correlated to space and location. Hidden Markov Models (HMMs) are useful to find and measure differences between dangerous stretches along highways. Here we use 2-state HMMs with Poisson, Borel-Tanner and Lagrange Poisson distributions, fitted to Brazilian highway accident data on route BR-381. This dataset lists 1,379 accidents occurred along a 449.1-kilometer segment of BR-381, stretching from Belo Horizonte to Extrema, both being cities in Minas Gerais state, in southeast Brazil. The data is over-dispersed and gives accident counts in sections of 0.1-kilometer granularity, so there are 4,491 spots with accident counts. MLE estimation of the parameters in HMMs with these 3 distributions is obtained by the EM Algorithm. HMMs with Lagrange-Poisson outperform other models. The dangerous sections (hot spots) are identified and the profile of safe locations is provided.