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Many topics social scientists study are sensitive in nature. Although we know some people may be reluctant to respond to sensitive questions in surveys, we know less about how such questions could influence responses to other questions appearing later in a survey. In this study, we use the Trump administration’s proposal to include a citizenship question on the 2020 Census to demonstrate how such spillover effects can undermine important survey-based estimates. Using a large survey experiment (n=9,035 respondents), we find that asking about citizenship status significantly increases the percentage of questions skipped and makes respondents less likely to report that members of their household are Hispanic. Not only does this demonstrate that sensitive questions can have important downstream effects on survey responses, but our results also speak to an important public policy debate that will likely arise in the future.