For Durham, if you are interested in individual case information, it's my understanding that you go to the Records Division at Durham Police Headquarters at 505 West Chapel Hill Street. According to their website, reports are available on weekdays between 7:30 a.m. and 5:00 p.m.
If you are just looking at crime trends, the Durham Crime Mapper is probably best to see robberies/larcenies in certain areas:
http://www.durhampolice.com/crimemapper.cfm