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The increased immigration in Western Europe has been linked by some political parties to increased criminality rates. We study the statistical relationship between the proportion of foreign-born to three types of reported criminality - rapes, burglary, and assault. The analysis is based on Swedish municipality level data for 2002–2014, years with significant immigration. Using non-parametric Gaussian processes models, we find that while reported rape rates have increased, they are likely best explained by changes in reporting. The reported burglary rates have decreased, while reported assault rates are positively correlated to the proportion of foreign-born residents in the municipality. [ABSTRACT FROM AUTHOR]