Science museums in Europe play an emerging and important role as brokers between the public and policy-making institutions and are becoming platforms that enable scientific citizenship. To do so, museums rely on the participation of their visitors. However, little is known about the relation between visitors’ interest to participate, their engagement with science, and their perceptions of the museum as a platform of scientific citizenship. This study analyzes visitors’ interest in 3 levels of participation: Sharing opinions and feedback (the museum as “forum”); co-developing programs and activities; and participating in the governance of the museum. Quantitative analysis of the data from a survey conducted among 364 adult visitors to the Science Museum in London reveals that interest in the forum function of the museum does not depend on visitors’ prior engagement with science, but rather on how the museum enables the scientific citizenship of its visitors. However, for interest in co-development the reverse was found—previous engagement and frequent visits are more important than scientific citizenship. The forum function of the museum and its perceived role in public policy further determine visitors’ interest in museum governance.