We consider a risk-sensitive optimal control problem for hidden Markov models (HMM). Building upon recent results by Baras, James and Elliott, we investigate the structure of risk-sensitive controllers for HMM, via an examination of a popular benchmark problem. We obtain new results on the structure of the risk- sensitive controller by first proving concavity and piecewise linearity of the value function. Furthermore, we compare the structure of risk-sensitive and risk-neutral controllers.