We address the problem of coordinating multiple agents in a dynamic police patrol scheduling via a Reinforcement Learning (RL) approach. Our approach utilizes Multi-Agent Value Function Approximation (MAVFA) with a rescheduling heuristic to learn dispatching and rescheduling policies jointly. Often, police operations are divided into multiple sectors for more effective and efficient operations. In a dynamic setting, incidents occur throughout the day across different sectors, disrupting initially-planned patrol schedules. To maximize policing effectiveness, police agents from different sectors cooperate by sending reinforcements to support one another in their incident response and even routine patrol. This poses an interesting research challenge on how to make such complex decision of dispatching and rescheduling involving multiple agents in a coordinated fashion within an operationally reasonable time. Unlike existing Multi-Agent RL (MARL) approaches which solve similar problems by either decomposing the problem or action into multiple components, our approach learns the dispatching and rescheduling policies jointly without any decomposition step. In addition, instead of directly searching over the joint action space, we incorporate an iterative best response procedure as a decentralized optimization heuristic and an explicit coordination mechanism for a scalable and coordinated decision-making. We evaluate our approach against the commonly adopted two-stage approach and conduct a series of ablation studies to ascertain the effectiveness of our proposed learning and coordination mechanisms.