Laser recrystallized low temperature poly-silicon films have attracted attention for their applications in thin-film transistors (TFTs), which are widely used in active matrix displays. The electrical characteristics of the poly-silicon film may vary because of its grain boundaries. In this work, the variation is statistically studied with respect to the threshold voltage and mobility of the TFTs. The threshold voltage and mobility of many closely-located TFTs are measured. These two parameters correspond to the deep states and tail states of the poly-silicon film, respectively. The mutual difference of two threshold voltages exhibits the distribution in a Gaussian-Lorentzian cross product form. On the other hand, the mutual difference of two mobility exhibits the distribution of Lorentzian function. This result directly reflects the local fluctuations and the spatial trends of the deep and tail states in a poly-silicon film.