A second-order control system with a saturating controller and a random disturbance is investigated. It is known that when the control signal preceding the saturator is a linear combination of state coordinates, the steady-state probability density in state space may be obtained by solution of the Fokker-Planck equation. In the present note it is shown that when the mean-square-error is minimized the saturator operates as a relay ; and the optimal parameter of the switching line is calculated. The explicit results obtained make the system a useful test case for computational solutions of the Fokker-Planck equation, and in other investigations of non-linear stochastic control systems.