Emerging research has shown that humans can form emotional attachment to Conversational Artificial Intelligence (CAI) through interaction with the system. CAI refers to the systems that mimic human conversations, which are increasingly capable of providing personalized and emotional responsiveness. The attachment to CAI possibly brings about benefits and risks to individuals' mental health. According to attachment theory, attachment has four features, including safe haven (i.e., turning to attachment figures for a sense of safety during times of distress), secure base (i.e., obtaining confidence from attachment figure for active exploration and personal growth), proximity-seeking (i.e., maintaining or restoring closeness to the attachment figures), and separation anxiety (i.e., feeling uneasiness and distress when attachment figure is unavailable). However, past studies usually consider attachment to CAI as a unidimensional construct; little is known about which features are more associated with mental health outcomes. To fill this gap, we examined the associations between the four features of attachment to CAI and six indicators of mental health (i.e., problematic CAI use, depression, anxiety, life satisfaction, positive affect and negative affect) using psychological network analysis based on a group of young frequent CAI users (N = 399, Mean age = 22.9, SD = 2.09, female N = 264). The results showed that problematic CAI use showed partial correlations with all features except for secure base, with the strongest correlation to separation anxiety. Depression showed a positive partial correlation with separation anxiety only, life satisfaction showed a positive partial correlation with secure base only, and positive affect showed a positive partial correlation with proximity seeking. Anxiety and negative affect showed minimal partial correlations. The nuanced results highlight the differential roles of four attachment features in mental health outcomes, suggesting a need to elucidate the benefits and risks associated with CAI attachment by looking at its different manifestations.