CHICAGO—The Chicago Police Department is nearly two weeks into its investigation of an alleged attack on Jussie Smollett, a star of the TV hit “Empire,” and has gathered little traction.

Police continue to review security camera footage and are trying to identify two people of interest seen walking down the sidewalk in one video. Their faces are silhouetted and not recognizable. Investigators haven't yet found footage of the attack.

“We’re looking at shreds of detail,” police spokesman Anthony Guglielmi said. “We’re painfully slow because we’re methodical.”

Investigators are also paying a lot of attention to a rope used in the attack, Mr. Guglielmi said. They have identified the retailers who sell that rope and will follow any leads found at those places, including on surveillance videos.

Mr. Smollett reported being attacked by two men yelling racist and antigay slurs, the Chicago Police Department said. Chicago police have said they have no reason to doubt Mr. Smollett’s account.