This paper studies an integrated sensing and communication (ISAC) system for single-target detection in a cloud radio access network architecture. The system considers downlink communication and multi-static sensing approach, where ISAC transmit access points (APs) jointly serve the user equipments (UEs) and optionally steer a beam toward the target. A centralized operation of cell-free massive MIMO (multiple-input multiple-output) is considered for communication and sensing purposes. A maximum a posteriori ratio test detector is developed to detect the target in the presence of clutter, so-called target-free signals. Moreover, a power allocation algorithm is proposed to maximize the sensing signal-to-interference-plus-noise ratio (SINR) while ensuring a minimum communication SINR value for each UE and meeting per-AP power constraints. Two ISAC setups are studied: i) using only existing communication beams for sensing and ii) using additional sensing beams. The proposed algorithm's efficiency is investigated in both realistic and idealistic scenarios, corresponding to the presence and absence of the target-free channels, respectively. Although detection probability degrades in the presence of target-free channels that act as interference, the proposed algorithm significantly outperforms the interference-unaware benchmark by exploiting the statistics of the clutter. It has also been shown that the proposed algorithm outperforms the fully communication-centric algorithm, both in the presence and absence of clutter. Moreover, using an additional sensing beam improves the detection performance for a target with lower radar cross-section variances compared to the case without sensing beams.

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