In recent years there has been an increasing research interest aimed at the development of innovative integrated optic gyroscopes. Some authors have investigated coupled-resonator waveguiding structures formed by microrings mainly for their capability of manipulating light velocity, proposing also their application in phasesensitive optic gyroscopes. In this work we analyze the main performance parameters of an integrated optic gyroscope consisting of a three coupled ring resonator structure having different radii and coupling coefficients. The main result is the enhancement of the scale factor of the multi-ring-based gyroscope, without increasing the overall footprint, with respect to a conventional single ring resonator gyro. The final sensitivity of the gyroscope is also evaluated and compared with the conventional integrated optic gyroscope configuration.