This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of Attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates,the proposed result.