We consider analysis and design of distributed filters for continuoustime stochastic systems, where the partial information about the states is measured by a distributed set of sensor units. These units are represented by nodes in an undirected and connected graph, whose edges represent the communication links between sensor units. It is stipulated that the communication between sensor nodes is time-sampled randomly and the sampling process is described by a Poisson counter. Our proposed filtering algorithm for each sensor node is a stochastic hybrid system: It comprises a continuous-time differential equation, and at random time instants when communication takes place, each sensor node updates its state estimate based on the information received by its neighbors. For this setup, we compute the expectation of the error covariance matrix for each node which is governed by a matrix differential equation, and relate its convergence with the mean sampling rate.