  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) ns
and 47.9(7)~ns, respectively. The ratio of these values is in good agreement
with scaling for the different excitation energies. The investigated molecular
states are of relevance for an experimental search for a permanent electric
dipole moment (EDM) of the electron in BaF.
