Control of seismic response of a building fitted with magnetorheological dampers is considered using Optimal Static Output Feedback (OSOF) for desired damper forces. The Modified Bouc-Wen damper model is used and two control voltage laws based on the MR constraint filter, i.e., Semi-inverse Quadratic Voltage Law and Semi-inverse On-Off Voltage Law, are proposed. These appear to perform at least as well as an existing Clipped Voltage Law. Comparisons with available results from a robust reliability-based controller show OSOF control to be quite effective. Controlled response using OSOF is compared with Linear Quadratic Guassian (LQG) and passive-on controllers. Moderate to substantial reduction in maximum peak/RMS responses is mostly obtained with base configuration of sensors when using OSOF control, and controller CPU time reduces by two orders of magnitude. Parametric studies regarding sensor configuration and state/control weighting matrices are performed in order to obtain effective control. Effective OSOF control requires drift feedback with drift sensor preferably collocated with damper.