Expressions are derived for the influence of a finite predissociation lifetime on the recoil anisotropy (beta parameter) from a symmetric top parent molecule. Tt is found that quantum interference between transitions is important. Application of these results explains an apparent anomaly in recent measurements of the state-to-state anisotropy for NH3 photodissociation. The theory in the limit of a long lifetime is then extended to molecules of low symmetry, showing that in favorable cases it is possible to obtain projections of the anisotropy onto more than one body-fixed axis. This has been applied to new measurements on the photodissociation process HFCO ((A) over tilde(1)A '') --> H(S-2) + FCO ((X) over tilde(2)A'), which has been studied for excitation through rotationally structured bands in the region of 250 nm. The use of selected rotational transitions in this asymmetric top has resulted in the determination of the second moments of the recoil anisotropy of the H atoms with respect to all three inertial axes (a, b, and c). This information provides strong evidence that the predissociation is mediated by intersystem crossing to the lowest triplet state (T-1).