Recent evidence for bimolecular nonradiative recombination in lead-halide perovskites poses the question for a mechanistic origin of such a recombination term. A possible mechanism is Auger recombination involving two free charge carriers and a trapped charge-carrier. To study the influence of trap-assisted Auger recombination on bimolecular recombination in lead-halide perovskites, we combine estimates of the transition rates with a detailed balance compatible approach of calculating the occupation statistics of defect levels using a similar approach as for the well-known Shockley-Read-Hall recombination statistics. We find that the kinetics resulting from trap-assisted Auger recombination encompasses three different regimes: low injection, high injection, and saturation. Although the saturation regime with a recombination rate proportional to the square of free carrier concentration might explain the nonradiative bimolecular recombination in general, we show that the necessary trap density is higher than reported. Thus, we conclude that Auger recombination via traps is most likely not the explanation for the observed nonradiative bimolecular recombination in CH3NH3PbI3 and related materials.