Chicago police and prosecutors on Tuesday interviewed the two brothers who purchased the rope used in the alleged racist and antigay attack reported by “Empire” actor Jussie Smollett last month, authorities said.

The brothers were initially questioned last week as potential suspects but were later released without being charged.

The two men, who are black, told police they purchased a rope that Mr. Smollett says was strung around his neck the morning he reported being attacked by a pair of men yelling racial and gay slurs, according to a person at the police department familiar with the investigation. The men, one of whom has appeared on “Empire,” told investigators they were paid, the person said.

Police have asked to speak with Mr. Smollett again as they now investigate whether he arranged the attack, according to another person familiar with the matter. No date has been set for that interview.

Also on Tuesday, police investigated but ultimately dismissed a tip that the brothers had been seen with Mr. Smollett in an elevator in his building.