On Nov. 11, a 51-year-old homeless man named Ramon Rivera who had been charged with stealing a $1,500 acrylic bowl from a fancy furniture store in Manhattan had a court-ordered appointment scheduled with his case manager.

He did not show up, according to two people familiar with the matter.

A week later, Mr. Rivera went on a rampage, randomly stabbing three people to death as he stalked across Manhattan, the authorities say. He was indicted Friday on three counts of first-degree murder.

Mr. Rivera’s apparent descent into homicidal madness shows the difficulty that the medical and legal systems have in keeping track of some of the city’s least stable people and ensuring they stay connected to care.

Mr. Rivera, who had a lengthy, if modest, criminal history and who legal documents say suffers from schizophrenia, had been in a court program called “supervised release” that is designed only to make sure that a defendant shows up for court appearances. He was required to attend two in-person sessions with a case manager, complete two phone check-ins and go to therapy in the first month. That schedule was one of the strictest available under the supervised release program.

When Mr. Rivera was released from jail last month after serving nine months for theft, he was referred to the city’s homeless shelter system. Over the next month, he spent only three nights in a shelter, according to someone familiar with his social service records.

Before he arrived in New York last year, Mr. Rivera lived in Florida and Ohio and had a criminal record that included at least two assault charges, one of which led to a 28-day stay at a psychiatric hospital. His recent sentence at the city’s Rikers Island jail complex was interrupted by two stints in the psychiatric unit of the Bellevue Hospital prison ward. During one of those stints, he assaulted a correction officer, according to records from the city’s Correction Department.