This research develops a method for trajectory planning of robotic systems with differential constraints based on hierarchical partitioning of a continuous state space. Unlike conventional roadmaps which is constructed in the configuration space, the proposed state roadmap also includes additional state information, such as velocity and orientation. A bounded domain of the additional state is partitioned into sub-intervals with multiple resolution levels. Each node of a state roadmap consists of a fixed position and an interval of additional state values. A valid transition is defined between a pair of nodes if any combination of additional states, within their respective intervals, produces a trajectory that satisfies a set of safety constraints. In this manner, a trajectory connecting arbitrary start and goal states subject to safety constraints can be obtained by applying a graph search technique on the state roadmap. The hierarchical nature of the state roadmap reduces the computational cost of roadmap construction, the required storage size of computed roadmaps, as well as the computational cost of path planning. The state roadmap method is evaluated in the trajectory planning examples of an omni-directional mobile robot and a car-like robot with collision avoidance and various types of constraints.