Our study aims to understand if users have concerns when communicating with a mental health chatbot and what information users would disclose to such bots. We have iteratively developed a survey collecting information about participant demographics, previous exposure to any mental health chatbots, what information participants would hypothetically disclose to mental health chatbots, and any concerns participants have about the chatbots. Our results show a statistically significant difference between a chatbot and non-chatbot users when it came to chatbot users' willingness to disclose to mental health chatbots, perceived risk of adverse security incidents and perceived precautions they would take when using mental health chatbots. Additionally, we found no significant differences between the two groups when it came to the perceived likelihood of adverse security events and the differences between knowledge of chatbots. These findings show the importance of including best security practices in mental health chatbots to protect existing vulnerable users and to allow new users to feel comfortable benefiting from the chatbots.