We study the properties of polarization evolution in sinusoidally spun fibers. It is found that, similar to linear birefringent fibers, the evolution of the state of polarization exhibits periodicity, which can be measured by distributed measurement, such as those made with a polarization optical time domain reflectometer. The spatial period is linked with the spin parameters and fiber beat length in a simple equation. In combination with a previous finding, it is shown that the spatial period is uniquely related to spun-fiber polarization mode dispersion. This suggests that distributed fiber polarization mode dispersion can be determined throughthe measurement of the spatial period obtained in a distributed measurement.