The times of flight of an atomic Bose-Einstein condensate are theoretically investigated in the experimentally unexplored regime corresponding to detection close to the trap of the condensate. In this regime, there is no consensus on how to calculate the distribution of times of arrival onto the detector. For non-interacting particles, distinct theoretical predictions have been made in the past. This work analyzes how these predictions are modified for an interacting Bose-Einstein condensate. For this purpose, a time-dependent Gross-Pitaevskii equation is solved analytically and numerically.