Even if several algorithms were proposed in the literature to solve the coverage problem in Wireless Sensor Networks (WSNs), they still suffer from some weaknesses. This is the reason why we suggest in this paper, a distributed protocol, called Single Phase Multiple Initiator (SPMI). Its aim is to find Connect Cover Set (CCS) for assuring the coverage and connectivity in WSN. Our idea is based on determining a Connected Dominating Set (CDS) which has a minimum number of necessary and sufficient nodes to guarantee coverage of the area of interested (AI), when WSN model is considered as a graph. The suggested protocol only requires a single phase to construct a CDS in distributed manner without using sensors’ location information. Simulation results show that SPMI assures better coverage and connectivity of AI by using fewer active nodes and by inducing very low message overhead, and low energy consumption, when compared with some existing protocols.