Lead-free perovskite halide CsSnI_{3} has emerged as a promising material for optoelectronic applications due to its direct bandgap (1.3-1.4 eV), high charge carrier mobility, and strong visible-spectrum absorption. Among its polymorphs, the green phase, with a favorable bandgap of \sim1.24 eV, demonstrates enhanced structural stability and resistance to phase degradation under ambient conditions. In this study, we investigate the green polymorph of CsSnI_{3} and observe pyroelectric behavior, indicative of ferroelectric-like properties despite its globally centrosymmetric (Pa\overline{3}) cubic structure. Utilizing Piezo-force microscopy, dielectric measurements, impedance spectroscopy, and Raman spectroscopy, we identified local non-centrosymmetry influencing hysteresis and conduction properties. Impedance spectroscopy further reveals the interaction of grains and grain boundaries under a low AC electric field, both before and after light exposure and poling. A reduction in relaxation time with increasing temperature in poled samples is observed, while the combined effects of light exposure and poling result in an increased relaxation time. Our results indicate that local non-centrosymmetry plays a critical role in influencing hysteresis and conduction behavior. These findings highlight the importance of phase transitions and vibrational mode dynamics in optimizing the performance of CsSnI_{3}-based devices, paving the way for their broader application in advanced optoelectronic technologies. mechanism and I-V hysteresis. This study highlights that local alterations in vibration modes significantly impact the current-voltage hysteresis and conduction behavior of perovskite halides, suggesting the presence of local non-centrosymmetry within the globally centrosymmetric CsSnI_{3}.