The incident began around 12:30 a.m. Century Park Place Apartments on Langdon Drive.
Officers said the man - who appeared to be armed with a long-barreled gun - also started yelling at police and throwing household items out of the window to the ground below.
"He was calling the white police officers colonizers, he was telling the black police officers they were on the wrong side," neighbor and eyewitness, Jaret Hodges said.
Several homes nearby were evacuated as a precaution; EMS and fire crews were also called to the scene.
The man was arrested and taken into custody; he has yet to be identified.
#BREAKING Exclusive #abc11 video shows the man involved in standoff w/@DurhamPoliceNC as they take him into custody. Watch cmdr tells me he was taken to hospital for treatment of cuts on hands, not confirming discovery of any weapon in apartment yet. pic.twitter.com/l1LpaXCqYj— Anthony Wilson (@AnthonyABC11) February 20, 2018
Police also said he is being treated for cuts on his hands, which may have been caused by the broken glass.