Conversational Artificial Intelligence (AI) is digital agents that interact with users by natural language. To advance the understanding of trust in conversational AI, this study focused on two humanness factors manifested by conversational AI: speaking and listening. First, we explored users' heterogeneous perception patterns based on the two humanness factors. Next, we examined how this heterogeneity relates to trust in conversational AI. A two-stage survey was conducted to collect data. Latent profile analysis revealed three distinct patterns: para-human perception, para-machine perception, and asymmetric perception. Finite mixture modeling demonstrated that the benefit of humanizing AI's voice for competence-related trust can evaporate once AI's language understanding is perceived as poor. Interestingly, the asymmetry between humanness perceptions in speaking and listening can impede morality-related trust. By adopting a person-centered approach to address the relationship between dual humanness and user trust, this study contributes to the literature on trust in conversational AI and the practice of trust-inducing AI design.