Opioid overdose rescue is very time-sensitive. Hence, drone-delivered naloxone has the potential to be a transformative innovation due to its easily deployable and flexible nature. We formulate a Markov Decision Process (MDP) model to dispatch the appropriate drone after an overdose request arrives and to relocate the drone to its next waiting location after having completed its current task. Since the underlying optimization problem is subject to the curse of dimensionality, we solve it using ad-hoc state aggregation and evaluate it through a simulation with higher granularity. Our simulation-based comparative study is based on emergency medical service data from the state of Indiana. We compare the optimal policy resulting from the scaled-down MDP model with a myopic policy as the baseline. We consider the impact of drone type and service area type on outcomes, which offers insights into the performance of the MDP suboptimal policy under various settings.