This article is concerned with the problem of recursive state estimation for a class of multirate multisensor systems with distributed time delays under the round-robin (R-R) protocol. The state updating period of the system and the sampling period of the sensors are allowed to be different so as to reflect the engineering practice. An iterative method is presented to transform the multirate system into a single-rate one, thereby facilitating the system analysis. The R-R protocol is introduced to determine the transmission sequence of sensors with the aim to alleviate undesirable data collisions. Under the R-R protocol scheduling, only one sensor can get access to transmit its measurement at each sampling time instant. The main purpose of this article is to develop a recursive state estimation scheme such that an upper bound on the estimation error covariance is guaranteed and then locally minimized through adequately designing the estimator parameter. Finally, simulation examples are provided to show the effectiveness of the proposed estimator design scheme.