We have computed the spectra of resonance states for several open quantum dot systems. These states are identified using the electron dwell time. The statistics of the spectra are exactly the same as that of the corresponding closed system, even when the level widths are comparable with the average spacing. In particular, for a regular structure, e.g., an open rectangular quantum dot, the resonance state level spacing satisfies the Poisson distribution. For an irregular structure, e.g., an open Sinai billiard, we found that the spacings satisfy the GOE or GUE statistics depending on whether an external magnetic field is applied. Thus in this regime of ballistic transport, the statistics of resonance transmission contains characteristics of the corresponding intrinsic quantum level distribution. \textcopyright{} 1996 The American Physical Society.