Time-resolved detection of laser-induced fluorescence from pulsed excitation of electronic states in barium monofluoride (BaF) molecules has been performed in order to determine the lifetimes of the A (2)Pi(1/2) and A (2)Pi(3/2) states. The method permits control over experimental parameters such that systematic biases in the interpretation of the data can be controlled to below 10(-3) relative accuracy. The statistically limited values for the lifetimes of the A (2)Pi(1/2) (nu = 0) and A (2)Pi(3/2) (nu = 0) states are 57.1(3) and 47.9(7) ns, respectively. Although discrepancies between presently and previously measured lifetimes and theoretical values persist, the ratio of these values is in good agreement with scaling for the different excitation energies. The results serve as a benchmark for current molecular structure calculations. The investigated molecular states are of relevance for an experimental search for a permanent electric dipole moment of the electron in BaF.