This paper investigates multi-target detection in an integrated sensing and communication (ISAC) system within a cell-free massive MIMO (CF-mMIMO) framework. We adopt a user-centric approach for communication user equipments (UEs) and a distributed sensing approach for multi-target detection. A heuristic access point (AP) mode selection algorithm and a channel-aware distributed sensing scheme are proposed, where local measurements at receive APs (RX-APs) are weighted based on the received signal's signal-to-interference ratio (SIR). A maximum a posteriori ratio test (MAPRT) detector is applied under two awareness levels at RX-APs. To balance the communication-sensing trade-off, we develop a power allocation algorithm to jointly maximize the minimum detection probability and communication signal-to-interference-plus-noise ratio (SINR) while satisfying power constraints. The proposed scheme outperforms non-weighted methods. Adding test statistics from more RX-APs can degrade sensing performance due to weaker channels, but this effect can be mitigated by optimizing the weighting exponent. Additionally, assigning more sensing RX-APs to a sensing area results in approximately 10dB loss in minimum communication SINR due to limited communication resources.