Conversational agents are increasingly used to substitute or augment human service employees. Due to their ability to use human‐like communicative behaviors, these agents are theorized to establish social connections with customers. However, the existing literature is ambiguous on how conversational agents should verbally communicate with customers and whether they should be adaptive to customers' verbal behavior. The current study aims to address these gaps, by focusing on the effects of the conversational agent's communication style on the perceived social connection. Two experiments were conducted in which a virtual agent in a hedonic service (Experiment 1) or a utilitarian service (Experiment 2) was manipulated to adapt either a static task‐ or a social‐oriented communication style or mimic the communication style used by the customer in the previous turn. Guided by marketing and human–computer interaction literature, measures for engagement and rapport were used to reveal customers' perceived social connection. Results show that for the hedonic service, rapport was significantly affected by the presence of social cues in the agent's communication style (whether statically or mimicked), while engagement was significantly affected by mimicry. For the utilitarian service, only social cues significantly affected rapport. These findings enrich the Computers As Social Actors paradigm and provide clear guidelines for practitioners.