In clinical studies, chatbots mimicking doctor-patient interactions are used for collecting information about the patient's health state. Later, this information needs to be processed and structured for the doctor. One way to organize it is by automatically filling the questionnaires from the human-bot conversation. It would help the doctor to spot the possible issues. Since there is no such dataset available for this task and its collection is costly and sensitive, we explore the capacities of state-of-the-art zero-shot models for question answering, textual inference, and text classification. We provide a detailed analysis of the results and propose further directions for clinical questionnaire filling.