Resonator integrated optic gyro (RIOG) is a high-accuracy gyroscope based on the Sagnac effect. The waveguide-type ring resonator is a key rotation sensing element in the RIOG. An asymmetric resonance line shape is found in the optic resonator. These asymmetries will induce offset errors when the phase modulation spectroscopy technique (PMST) is applied to the RIOG. The polarization errors and the difference among normal mode losses are found to be the two main sources of resonance asymmetry in an experiment. These sources are fully investigated and their contributions to the offset errors are compared. The analysis shows that proper modulation frequencies in clockwise (CW) and counterclockwise (CCW) directions can reduce an RIOG bias error. A transmissive resonator is recommended to obtain a better resonance line shape.