API search involves finding components in an API that are relevant to a programming task. For example, a programmer may need a function in a C library that opens a new network connection, then another function that sends data across that connection. Unfortunately, programmers often have trouble finding the API components that they need. A strong scientific consensus is emerging towards developing interactive tool support that responds to conversational feedback, emulating the experience of asking a fellow human programmer for help. A major barrier to creating these interactive tools is implementing dialogue management for API search. Dialogue management involves determining how a system should respond to user input, such as whether to ask a clarification question or to display potential results. In this paper, we present a dialogue manager for interactive API search that considers search results and dialogue history to select efficient actions. We implement two dialogue policies: a hand-crafted policy and a policy optimized via reinforcement learning. We perform a synthetics evaluation and a human evaluation comparing the policies to a generic single-turn, top-N policy used by source code search engines.