This paper studies market segmentation that arises from the introduction of a price ceiling in the market for rental housing. When part of the market faces rent control, theory predicts an increase of free-market rents, a consequence of misallocation of households to housing units. We study a large-scale policy intervention in the German housing market in 2015 to document this mechanism empirically. To identify the effect we rely on temporal variation in treatment dates, combined with a difference-in-differences setup and a discontinuity-intime design. By taking a short-run perspective, we are able to isolate the misallocation mechanism from other types of spillovers. We find a robust positive effect on free-market rents in response to the introduction of rent control. Further, we document that rent control reduced the propensity to move house within rent controlled areas, but only among highincome households. Interpreted through the lens of our theoretical model, this spillover is a clear sign of misallocation. Further, we document that the spillover brings forward demolitions of old, ramshackle buildings.