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This paper presents a method for the optimal state assignment of asynchronous state machines. Unlike state assignment for synchronous state machines, state codes must be chosen carefully to ensure the avoidance of critical races and logic hazards. Two related problems are considered: (i) optimal critical race-free state assignment; and (ii) optimal hazard-free and critical race-free state assignment for normal fundamental mode machines. Analogous to a paradigm successfully used for the optimal state assignment of synchronous machines each problem is formulated as an input encoding problem. Solutions are targeted to sum-of-products implementations. Initial results indicate output logic improvements up to 20% for the hazard-free algorithm, and more modest improvement for the optimal critical race-free algorithm.