This fact counters the narrative in Europe and America that refugees and immigrants are all big time criminals, and that we shouldn't accept them as a result. I actually decided to write this post after watching people on r/PoliticalCompassMemes make downright racist comments about refugees under the guise of joking. Before we get started, you should keep in mind that these people are fleeing literal war crimes and and repression from a dictatorial regime. Show some empathy.

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So let's get started:

This paper finds that Germans were not "victimized in greater numbers by refugees as measured by their rate of victimization in crimes with refugee suspects".

This paper talks about why German crime stats in 2015 are poorly placed to draw conclusions from regarding influx of crime. It also finds that higher rates of crimes among asylum seekers are pretty much entirely in line with the demographic (i.e. younger men) and estimate that most of the crime is refugee-on-refugee.

The German media also has a tendency to "distort" crime rates by focusing on crimes committed by refugees, rather than crimes that are also committed against them.

There have been a number of studies done on the influx of asylum seekers to Germany, which find that there was not a significant upshot in crime. This paper finds "very small increases in crime in particular with respect to drug offenses and fare-dodging." which whoop-de-doo, I'm not going to force, through state violence, someone to stay within a warzone where there is active genocide taking place because I'm worried about fare-dodging. This paper finds that asylum seekers don't impact crime rates and recognized refugee crime rates are driven by non-violent property crimes and frauds.

This paper from Germany finds that the arrival of nearly one million refugees to Germany in 2015 did not increase Germans' likelihood of being victims of crime (including robbery, sexual assault and violent crimes). This article also finds that refugees did not increase crime in Germany.

This voxeu article finds that during the refugee crisis, more than 600,000 migrants crossed the Mediterranean and took up residence in Italy. This led to increased spending for police protection, not because of higher crime rates, but to the deterioration of social capital and unfounded fears of criminality.

Also in Italy, this paper finds that:

we use instrumental variables based on immigration toward destination countries other than Italy to identify the causal impact of exogenous changes in Italy’s immigrant population. According to these estimates, immigration increases only the incidence of robberies, while leaving unaffected all other types of crime. Since robberies represent a very minor fraction of all criminal offenses, the effect on the overall crime rate is not significantly different from zero.

This paper (PDF warning) is quite interesting. It finds only a minor increase in crime, with no detectable increase in violent crime, associated with asylum seekers. Quite importantly, the level of crime is strongly co-related with whether the asylum seeker is from a "low-protection" or a "high-protection" country. Low protection means the asylum seeker is from a country where there length of stay in Germany is less likely to be guaranteed - i.e. from Russia and they may be found they have to return - whereas a high-protection country is one where they are unlikely to be sent back to - sending many migrants back to Syria is giving them a death sentence, so they are allowed to stay in Germany long-term. These long term, more secure, migrants are less likely to commit crimes.

By excluding the importance of alternative channels one by one, we argue that it is indeed the perspective of being able to stay in the host country and to access its labor market which is a key determinant of criminal activity. It should therefore be considered in future analyses. This result allows predictions about which groups of immigrants are most prone to commit crimes in the host country. It also allows policy makers to target police efforts as well as integration measures and changes in the law for asylum towards the different groups.

So the integration policy of a country impacts crime rates by refugees. Makes sense that most refugees who commit crime are the ones who aren't allowed to work.

This paper found that Trump's refugee ban (which resulted in a 65% reduction in refugee arrivals) had no discernible impact on county-level crime rates.

This paper finds no evidence of a link between refugees and crime in America.

This relatively new book finds that the evidence does not substantiate the conjecture that refugee migration to EU countries led to increases in crime (whether it's burglary, robbery, vehicle theft, drug, assault, homicide, rape, or sexual assault).

Some extra studies by PewResearch center:

She begins her analysis by noting this well-documented phenomenon: The crime rate among first-generation immigrants—those who came to this country from somewhere else—is significantly lower than the overall crime rate and that of the second generation. It’s even lower for those in their teens and early 20s, the age range when criminal involvement peaks.

But just a generation later, the crime rate soars. In fact, it is virtually identical to the rate among native-born Americans across the most crime-prone years. As the accompanying chart taken from an earlier Bersani study shows, about a quarter of 16-year-old native-born and second-generation immigrants have committed a crime in the past year. In contrast, about 17% of the foreign-born 16-year olds have broken the law

and ResearchGate:

For more than a century, innumerable studies have confirmed two simple yet powerful truths about the relationship between immigration and crime: immigrants are less likely to commit serious crimes or be behind bars than the native-born, and high rates of immigration are associated with lower rates of violent crime and property crime. This holds true for both legal immigrants and the unauthorized, regardless of their country of origin or level of education.

and from UC:

Given the cumulative weight of this evidence, the rise in immigration is arguably one of the reasons that crime rates have decreased in the United States over the past decade and a half—and even more so in cities of immigrant concentration. A further implication of this evidence is that if immigrants suddenly disappeared and the U.S. became immigrant-free (and illegal-immigrant free), crime rates would likely increase. The problem of crime and incarceration in the United States is not “caused” or even aggravated by immigrants, regardless of their legal status. But the uncritical and evidence-optional assumption that the opposite is true persists among policymakers, the media, and the general public, thereby impoverishing a genuine understanding of complex phenomena—a situation that undermines the development of evidence-based, reasoned public responses to both crime and immigration.

and lastly, from FSR:

this research suggests that immigrants are less, not more, criminal than non-immigrants, and that immigration rated are largely unassociated with crime rates.

TLDR; Immigrants, including undocumented and asylum seeking immigrants, do not commit more crime. Most evidence finds that refugees usually don't commit more crime, but it depends on the country's integration process. Countries that did I good job getting refugees jobs or welfare found no increase in crime, where as countries that did a terrible job found minor increases in crime. Additionally, it should be noted that even when they found mild increases in crime, the criminals are usually from an already high crime demographic, e.g young men, which explains it for the most part. Usually when they do commit crime, it doesn't target natives.

Bonus: As it turns out Immigrants actually spur natives to commit more crime in Germany. This study finds that increases in refugee migration to Germany is linked to greater right-wing hate crimes.