This paper is concerned with the distributed recursive state estimation problem for a class of multi-rate nonlinear systems over the sensor networks. The sensor nodes in the sensor network are communicated with each other through communication networks equipped with the FlexRay protocol, which is a hybrid protocol consists of both static and dynamic scheduling rules regulated by two time-varying variables within a communication cycle. The main purpose of this paper is to design local distributed state estimators by taking into account the scheduling of the FlexRay protocol. Upper bounds are first obtained on the local state estimation error covariances (EECs) by solving two matrix recursive equations, and then the minimum of the derived upper bounds are acquired through calculating adequate local gain matrices. Finally, the local estimates are fused by using the covariance intersection fusion method. Moreover, the uniform boundedness of the upper bounds on local EECs are analyzed. An illustrate example is provided to verify the effectiveness of the proposed distributed state estimation algorithm.