  We have investigated the threshold of photodetachment of Li^- leading to the
formation of the residual Li atom in the $2p ^2P$ state. The excited residual
atom was selectively photoionized via an intermediate Rydberg state and the
resulting Li^+ ion was detected. A collinear laser-ion beam geometry enabled
both high resolution and sensitivity to be attained. We have demonstrated the
potential of this state selective photodetachment spectroscopic method by
improving the accuracy of Li electron affinity measurements an order of
magnitude. From a fit to the Wigner law in the threshold region, we obtained a
Li electron affinity of 0.618 049(20) eV.
