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Joint reduced-state detection and group decoding (RSD-GD) is a promising approach to increase the spectral efficiency of multiple-access systems. Performance of RSD-GD receivers improves as coding information of more users is taken into account in the detection algorithm. For asynchronous channels, however, there is another approach to improve performance: use of more states of the multiple-access channel (MAC). Performance of RSD-GD receivers for asynchronous channels has been investigated using computer simulations; however, analytical studies of the performance of RSD-GD have not been reported so far. In this paper we derive upper bounds for the performance of RSD-GD over asynchronous MAC. The new results are based on an improved upper bound on the error event probability, which is significantly tighter than the traditional bound based on pairwise error events. Comparisons with values obtained from computer simulations show the excellent accuracy of the proposed bound.