Periodic applications involve tasks that execute continuously at specific intervals, often leading to concurrency-related data races. Traditionally, locks are used as synchronization mechanisms to ensure correctness. However, in safety-critical systems, a low-priority task holding a lock may be preempted by a high-priority task that requires the same lock, resulting in priority inversion and violating the periodicity and priority of high-priority tasks. While previous research has focused on race detection techniques for applications without nested locking, these approaches fail to generalize to scenarios involving nested locks. This work introduces a worst-case response time analysis and a robust technique for static race detection in periodic applications with nested locking behavior. The proposed algorithm provides a conservative upper bound for task response times while addressing the complexities of nested locks, enhancing the safety and dependability of concurrent periodic programs. Implemented in Rust, the algorithm is evaluated for performance and correctness across various programs, demonstrating its efficacy.