This paper presents a new recursive Hybrid consensus filter for distributed state estimation on a Hidden Markov Model (HMM), which is well suited to multirobot applications and settings. The proposed algorithm is scalable, robust to network failure and capable of handling non-Gaussian transition and observation models and is, therefore, quite general. No global knowledge of the communication network is assumed. Iterative Conservative Fusion (ICF) is used to reach consensus over potentially correlated priors, while consensus over likelihoods is handled using weights based on a Metropolis Hastings Markov Chain (MHMC). The proposed method is evaluated in a multi-agent tracking problem and a high-dimensional HMM and it is shown that its performance surpasses the competing algorithms.