DC is unique in not being part of any state. Congress rules it and federal law enforcement doesn’t need permission to operate there. They aren’t normally going to bother with local crime that the city force can handle. But it’s not surprising to see them interested in a high profile murder.
There are certainly plenty of federal LEOs in DC. More than 20 uniformed federal agencies operate there.
The point is what type of law was violated - local or federal - and a street robbery/murder is not a federal crime. The MPD investigates local crimes.