In the cell-free massive multiple-input multiple-output (CF mMIMO) system, the centralized transmission scheme is widely adopted to manage the inter-user interference. Unfortunately, its implementation is limited by the extensive signaling overhead between the central process unit (CPU) and the access points (APs). In this letter, we study the downlink transmission scheme in a distributed approach. First, we propose a reduced channel state information (CSI) exchange mechanism, where only the CSI of a portion of users is shared among neighboring APs. Base on this, the dual decomposition method is adopted to jointly optimize the precoder and power control. The precoding vector can be independently calculated by each AP cluster with closed-form expression. With very few iterations, the proposed distributed scheme achieves the same performance as the centralized one. Moreover, it significantly reduces the information exchange to the CPU.