Time resolution is a key parameter in the performance of a Time-of-Flight (TOF) Positron Emission Tomography (PET) scanner, and it is usually measured in the system with unscattered data and used as the width of the TOF kernel in reconstruction. In fact, the time distribution of detected coincidence events is a function of the energy of the detected photons, and true and scatter events have different time distributions. While the reconstruction TOF kernel should match the true or unscattered data, the scatter simulation used for scatter correction should match the time distribution of the scatter data. This work, using experimental measurements and Monte Carlo simulation, confirmed that the time resolution in a PET scanner is dependent on the energy of the detected photon pair. Moreover, it was observed that trues, single and multiple scatter in general have different time distributions. The full width half maximum (FWHM) of the time distribution of trues and scatter in different configurations of phantoms and energy threshold were evaluated. The width of the time distribution for scatter was observed to be much larger than for trues, particularly because of the effect of multiple scatter, if low energy thresholds are used. On the other hand, the use of high energy thresholds (for example, 435 keV) reduces the time distribution FWHM of the overall scatter and the amount of multiple scatter accepted: in that case, the single scatter simulation provides a good estimate of the experimental scatter time distribution. Moreover, at these high thresholds, the time distribution of the scatter becomes very close to that of the trues, and even using the trues time resolution for the scatter simulation will not produce a significant effect on the final image.