The resonator fiber optic gyroscope (RFOG) senses angular rotation by measuring the frequency shift between clockwise and counterclockwise resonances inside a fiber ring resonator (FRR). Three types of polarization-maintaining FRR are studied: normal FRR, FRR with 90° polarization-axis rotated splice, and FRR employing an in-line polarizer. We establish the models to analyze the output characteristics of the three FRRs, and present the experimental results for the three FRRs. In the normal FRR, the unwanted polarization state will destroy the symmetry of the resonance curve. In the FRR with 90° polarization-axis rotated splice, the unwanted and wanted polarization state coexist, and they do not overlap. In the FRR employing an in-line polarizer, the unwanted polarization state is completely suppressed, but the finesse of the FRR is also reduced.