The optimal filtering problem for a nonlinear stochastic system with a non-elliptic diffusion term is studied. Under a more general geometric assumption involving the system reachability, (which includes the strong elliptic case), a Zakai-like equation is derived, and the existence and unicity of the solution is proved. This equation results to be satisfied by a suitably defined unnormalized conditional probability density, from which the optimal state-estimate can be easily derived.