Does large-scale refugee immigration affect crime rates in receiving countries? We address this question based on the large and unexpected refugee inflow to Germany that peaked in 2015–2016. Arriving refugees were dispersed across the country based on a binding dispersal policy, yet we show that systematic regional sorting remains. Our empirical approach examines spatial correlations between refugee inflows and crime rates using the administrative allocation quotas as instrumental variables. Our results indicate that crime rates were not affected during the year of refugee arrival, but there was an increase in crime rates one year later. This lagged effect is small per refugee but large in absolute terms and is strongest for property and violent crimes. The crime effects are robust across specifications and in line with increased suspect rates for offenders from refugees’ origin countries. Yet, we find some indication of over-reporting.