This letter examines a state estimation with event-based transmissions for a linear discrete-time system when multiplicative noise affects the measurements while the additive noises of process and measurements of the sensor are correlated with each other. A general event-based technique is applied to produce the measurements at event-triggering instants and the sum of Gaussians approach is used at remote estimator to address the computation of state estimate when measurements are unavailable. The two-step predicted probability density function with Gaussian assumption is used to derive the recursive equations for the state estimate and its covariance matrix when the correlation between additive noises is at the same epoch. The results proposed are validated by a numerical example. © 2017 IEEE.