In this letter, we investigate a coordinated multiple point (CoMP)-aided integrated sensing and communication (ISAC) system that supports multiple users and targets. Multiple base stations (BSs) employ a coordinated power allocation strategy to serve their associated single-antenna communication users (CUs) while utilizing the echo signals for joint radar target (RT) detection. The probability of detection (PoD) of the CoMP-ISAC system is then proposed for assessing the sensing performance. To maximize the sum rate while ensuring the PoD for each RT and adhering to the total transmit power budget across all BSs, we introduce an efficient power allocation strategy. Finally, simulation results are provided to validate the analytical findings, demonstrating that the proposed power allocation scheme effectively enhances the sum rate while satisfying the sensing requirements.