Question answering (QA) over text passages is a problem of long-standing interest in information retrieval. Recently, the conversational setting has attracted attention, where a user asks a sequence of questions to satisfy her information needs around a topic. While this setup is a natural one and similar to humans conversing with each other, it introduces two key research challenges: understanding the context left implicit by the user in follow-up questions, and dealing with ad hoc question formulations. In this work, we demonstrate CROWN (Conversational passage ranking by Reasoning Over Word Networks): an unsupervised yet effective system for conversational QA with passage responses, that supports several modes of context propagation over multiple turns. To this end, CROWN first builds a word proximity network (WPN) from large corpora to store statistically significant term co-occurrences. At answering time, passages are ranked by a combination of their similarity to the question, and coherence of query terms within: these factors are measured by reading off node and edge weights from the WPN. CROWN provides an interface that is both intuitive for end-users, and insightful for experts for reconfiguration to individual setups. CROWN was evaluated on TREC CAsT data, where it achieved above-median performance in a pool of neural methods.