This paper investigates an adaptation of the Kalman filter for linear continuous-discrete system with multi-rate sampled outputs. The contribution of this article is twofold. First, we prove the exponential convergence of this observer through the existence of bounds for the Riccati matrix. Second, we highlight a technical point that allows us, under certain conditions on the sampling procedure, to prove the stability of the Riccati equation, and show that observability is preserved under multi-rate sampling. An example with two sensor outputs is given for illustration. This study can lead to applications in mobile robotics where sensors produce outputs at different rates and asynchronously.