Overtaking maneuver is one of the most dangerous scenarios for road vehicles especially in two-way roads. In this article, we propose a new formulation for the problem of overtaking in two-way roads using the tools from the Mixed Observable Markov Decision Process (MOMDP). This new formulation helps us to find the optimum strategy considering the uncertainties in the problem. Due to its computational complexity, solutions of Markov-based decision processes are very complicated, especially for the problems with measurement uncertainties. With the help of the efficient solvers and development and evolutions in computational technology, we show the applicability of Markov-based decision processes for the overtaking problem. The proposed method is tested in simulations and compared with other stochastic-variant Markov Decision Process (MDP) and classical time to collision (TTC) approaches. The proposed MOMDP solution improves the performance in comparison to both MDP and classical TTC approaches by lowering collision probability and overtaking duration.