We focus on a spectrum sharing based secondary cell-free system, which enables efficient utilization of the limited spectrum. For it, we develop a distributed downlink power allocation algorithm, in which each access point (AP) computes only its power coefficients locally, to improve energy efficiency (EE) while satisfying the interference constraints imposed by the primary system. Each AP solves smaller number of variables in parallel compared to centralized approach in which all power coefficients are computed centrally. Hence, it is computationally efficient and is scalable in terms of the number of APs. For the simulation setup considered with correlated Rayleigh fading, the proposed distributed approach achieves up-to 85% of the centralized EE. Furthermore, it achieves better performance compared to other distributed approaches.