As mentioned above, it depends on the type of crime, and the circumstances of those involved. If one just looks at the studies that show there is more crime in poverty-stricken neighborhoods, then this would imply that poor people are more likely to commit crimes, as if poor people have less morals. There is correlation, but correlation does not mean causation.
If we are speaking of violent crimes, then the correlation between poverty and crime may be there for reasons such as: desperation, unemployment, stress, lack of education, lack of opportunity, survival etc.
However, I do not believe it is the poverty alone that causes crime, it is the characteristics of the individuals, their family structure, their beliefs, self-control, personal goals, etc.
Millions of people are living in poverty, but only a small amount resort to crime. Many poverty-stricken people will work night and day just as hard as any higher income person, to try and provide an honest living for their families. The majority of people living in poverty would never resort to crime. Again, it's not simply the poverty, but the mentality, experiences, and values of the individuals.
Now higher income businesses and neighborhoods are also filled with crime, but different types of crimes on different scales. The kind of crime that is not as "sensational" as the more violent crimes, and also it's crime that may go un-prosecuted as it is more organized and perhaps harder and more time consuming to prove, than say a shooting. Examples: Extortion, bribery, insurance fraud, business scams, embezzlement, identity theft, theft, employee discrimination, tax evasion, money laundering, forgery etc.
As for people living in poverty who choose to commit violent crimes, giving them money would not magically change their character. Some would still find a way to commit some type of crime because that is who they have become.