One contribution to the time resolution of a scintillation detector is the signal time spread due to path length variations of the detected photons from a point source. In an experimental study a rectangular scintillator was excited by means of a fast pulsed ultraviolet laser at different positions along its longitudinal axis. Timing measurements with a photomultiplier tube in a detection plane displaced from the scintillator end face showed a correlation between signal time and tube position indicating only a small distortion of photon angles during transmission. The data is in good agreement with a Monte Carlo simulation used to compute the average photon angle with respect to the detection plane and the average propagation time. Limitations on timing performance that arise from propagation time dispersion are expected for long and thin scintillators used in future particle identification systems.