There was something in the newspaper a few weeks back about Katrina refugees in Dallas. There has been a mixed bag of results. First, there are the refugee on refugee crimes. Obviously, if they were not in Dallas, then Dallas would not have those crimes. You then have the locals who prey on the refugees in the form of opportunistic crime as can happy with high tourist areas that have a lot of non-local folks. You have refugee on locals crime where Katrina refugees were bad people at home are now bad people in their newly settled areas.
How does this figure with the Houston pawn shop shooting? Businesses do get robbed, regardless of whether they are in a town with lots of refugees or not. I don't think bad refugees will do more crime because they feel they are less likely to get caught. If that was the case, you would have a lot more of highly mobile roving bandits. There are some, of course, but most bad guys don't do it.
Then there are those that live in one place and do crime in another. For about the first 3 weeks of each new semester, the Bryan/College Station area (Texas A&M) would be hit with a rash of burgled cars, preference often (but not always) given to apartment complexes near the highway. Generally speaking, what you had was small bands of guys, usually out of Houston, but sometimes out of Austin who drive into town, burgle vehicles for a short period of time (1-3 hours) over several complexes and then head out of town. A given complex might get hit several times, but just a few cars at a time in those 3 weeks.