We explore biexciton (BX) nonradiative recombination processes in single semiconductor nanocrystals (NCs) using confocal fluorescence microscopy and second-order photon intensity correlation. More specifically, we measure the photoluminescence blinking and BX quantum yields (QYs) and study the correlation between these two measurements for single core (shell) CdSe (CdS) nanocrystals (NCs). We find that NCs with a high "on" time fraction are significantly more likely to have a high BX QY than NCs with a low "on" fraction, even though the BX QYs of NCs with a high "on" fraction vary dramatically. The BX QYs of single NCs are also weakly dependent upon excitation wavelength. The weak correlation between exciton "on" fractions and BX QYs suggests that multiple recombination processes are involved in the BX recombination. To explain our results, we propose a model that combines both trapping and an Auger mechanism for BX recombination.