Previous research has shown that the use of self-disclosure, the process of revealing personal thoughts and feelings, in conversational agents (CAs) increases overall user evaluations. However, research exploring the effects of self-disclosure in different situations or dialogue types is limited. This study investigated the effects of self-disclosure and dialogue type (task- vs. social-oriented) on trust, usefulness, and usage intention. Results showed significant interaction effects between self-disclosure and dialogue type. For CAs that did not use self-disclosure, trust, usefulness, and usage intention were higher in task-oriented dialogues. In contrast, CAs that did use self-disclosure had higher trust, usefulness, and usage intention in social-oriented dialogues. These results suggest that researchers and designers should consider the specific dialogue types and corresponding user goals when adding human qualities, such as self-disclosure, to CAs.