In this paper, we consider stationary hidden Markov models with finite state space and non parametric modeling of the emission distributions. We propose a new penalized least-squares estimator for the emission distri-butions which we prove to be asymptotically rate minimax adaptive up to a logarithmic term when there are two hidden states. This non parametric es-timator requires the computation of a preliminary estimator of the transition matrix of the hidden chain for which we propose to use the spectral estimator recently presented in [HKZ12]. We also investigate the asymptotic proper-ties of a spectral estimator of the emission distributions derived from that of [HKZ12]. The spectral estimator can not achieve the asymptotic minimax rate, but it is very useful to avoid initialization problems in our least squares minimization algorithm. Simulations are given that show the improvement obtained when applying the least-squares minimization consecutively to the spectral estimation.