Distributed filtering is crucial in many applications such as localization, radar, autonomy, and environmental monitoring. The aim of distributed filtering is to infer time-varying unknown states using data obtained via sensing and communication in a network. This paper analyzes continuous-time distributed filtering with sensing and communication constraints. In particular, the paper considers a building-block system of two nodes, where each node is tasked with inferring a time-varying unknown state. At each time, the two nodes obtain noisy observations of the unknown states via sensing and perform communication via a Gaussian feedback channel. The distributed filter of the unknown state is computed based on both the sensor observations and the received messages. We analyze the asymptotic performance of the distributed filter by deriving a necessary and sufficient condition of the sensing and communication capabilities under which the mean-square error of the distributed filter is bounded over time. Numerical results are presented to validate the derived necessary and sufficient condition.