It is true that the amount of trust the police force has with the community is key. It is also due to size, in my opinion. Small or close-knit communities look out for one another. They are more likely to see the police as neighbors and friends than in a big city, where they are seen as outsiders.
I think if you looked at statistics, there are certain kinds of communities which have similar experiences that do not always cooperate with law enforcement. Choosing to help the police or not really boils down to two things: experience and trust. If the only experiences people have with the police are negative, they will clearly be disinclined to help when the police ask them. For example, if the only time you ever see a policeman is when they want you rather than you wanting or needing them, it would be difficult to foster much trust in that relationship. In terms of trust, this, too, comes down to when and where and under what circumstances people have experienced the positive and negative aspects of the police.
There are a lot of different factors at play in a situation like that. Perhaps the police have a checkered history in the community (as the LAPD does in South Central Los Angeles, for example) and they do not trust the police overall. Perhaps the crime rate has been high enough that people believe the criminals have more power than law enforcement and they either do not believe that helping the police will do any good, or that it will bring retaliation from criminal elements.
Studies have shown that economically poorer neighborhoods tend to have less involvement with police efforts than those from more affluent neighborhoods, where the crime rate is probably less to begin with. The affluent have more education, more time on their hands, and a better tax base to support a well funded police department and patrols.
My understanding is that it has very much to do with the level of trust that the community has in their police department. In a typical affluent suburban community, the community feels that the police department is working for them and that their interests and wealth are protected by the police. They know that the police will have to respect the law regarding any actions in the community because they can afford to take legal action if any lines are crossed.
In a poorer urban community, there is far less trust between the community and the police as there is very much more of an us vs. them mentality. The community cannot rely on the protection of their rights because they cannot afford to fight against the resources of the police department, etc.