The general Jones matrix of the whole optical circuit in the resonator integrated optic gyro is deduced firstly, and then the propagation process of both polarization eigenstates in the gyro optic circuit is described by the matrix. The influence of refractive index difference between both polarization states, the coupling between both states in the cavity, the misalignment angle of fiber splices at the input and output port of the multifunction integrated optical device (MIOC) and the extinction ratio of MIOC, on the optical output properties of the resonator is analyzed.