Relatives of a black man who was led by rope down a street in Galveston, Tex., by two white police officers said Tuesday that the man has suffered from bipolar disorder and schizophrenia most of his life and regularly sleeps on the streets — struggles they said officers should have known about based on his criminal history.

The man, Donald Neely, 43, was arrested Saturday on a charge of criminal trespassing in a commercial neighborhood. The police said he had been warned several times before not to trespass in the area. When a police car was not immediately available, he was escorted by mounted police officers about four blocks to a nearby staging area, the Galveston Police Department said in a statement.

The scene was captured in a photograph by an onlooker and shared widely on social media, drawing national attention as it conjured for many images of slavery and mistreatment by whites of African-Americans.

Taranette Neely of Houston, Mr. Neely’s sister, said in an interview on Tuesday that Mr. Neely had been released 20 hours after his arrest.