The first is MPD's listserves. They have listserves for each district (we are in district 3) and they list all the crimes that happened each day, major arrests, info about suspects wanted, safety tips, and more. They're pretty useful. Here's the MPD page with all the listserves: Third District and Third District Substation cover Ward 1. (And here's the police district maps.)
The other option to get crime info is to use the city's online crime map. It's interesting, but a word of warning, it may freak you out. It's at crimemap.dc.gov -- although crime around 14th and Irving, for example, is down 12% from the same time last year, so that's a plus.