Monolithic gamma detector is gaining increasing interest due to its intrinsic DOI capability, lower cost and potentially better timing and energy resolution compared to conventional pixelated detector designs. In monolithic detector designs, it is preferable to perform a certain level of multiplexing to reduce the number of readout channels in real application. However, multiplexing comes with degradations of detector’s spatial resolution. The spatial resolution degradations under different multiplexing strategies need to be carefully evaluated. In this work, we studied the positioning performance of a monolithic gamma detector under different multiplexing strategies. The light response model (LRF) of the detector was generated with Monte Carlo simulation combined with experimentally calibrated energy response model. Based on the generated LRF, Cramer-Rao lower bound (CRLB) was used to evaluate the detector positioning performance under no multiplexing and six different multiplexing strategies including RCS-12, Diagonal-11, Square-9, Corner-9, RCS-6 and RCS-GAP-6. The results demonstrate that there is only slight positioning performance degradation from no multiplexing to RCS-12 with the average value of square root of CRLB from 0.35 mm to 0.45 mm in x direction and from 0.53 mm to 0.71 mm in z direction. However, if the readout channel number is further reduced to 9 (Square-9 or Corner-9) and 6 (RCS-6 or RCS-GAP-6), significant positioning performance degradations are observed. The positioning performance of Diagonal-11 is much poorer than that of RCS-12 though only one readout channel fewer. To conclude, RCS-12 is a promising multiplexing strategy with reversed detector positioning capability compared to no multiplexing and similar multiplexing approach could be used in other monolithic gamma detector designs. This work provides practical guidance in choosing multiplexing strategy to facilitate monolithic detector design.