We experimentally demonstrate a detection scheme suitable for state analysis of single optically trapped atoms in less than 1 μs with an overall detection efficiency η exceeding 98%. The method is based on hyperfine-state-selective photoionization and subsequent registration of the correlated photoion-electron pairs by coincidence counting via two opposing channel electron multipliers. The scheme enables the calibration of absolute detection efficiencies and might be a key ingredient for future quantum information applications or precision spectroscopy of ultracold atoms.