CHICAGO — Jussie Smollett, upset by his salary and seeking publicity, staged a fake assault a week after writing himself a threatening letter, the Chicago police said Thursday after the “Empire” actor surrendered to face a felony charge of filing a false police report.

The Chicago Police Superintendent Eddie T. Johnson, visibly angry at a morning news conference, said Mr. Smollett had taken advantage of the pain and anger of racism, draining resources that could have been used to investigate other crimes for which people were actually suffering.