FOR nearly 10 years, Marcus lived in a tiny cell in Sing Sing prison. His wife and children were eager for him to return to their home in public housing in Harlem. After he completed his sentence for attempted armed robbery and possession of stolen property, his parole board said he was ready to rejoin society. But the city’s public housing authority disagreed: Because Marcus — a pseudonym — had a criminal record, he was ineligible to live with his family.

Nationwide, more than 600,000 people return from prison each year and try to rebuild their lives. The only viable option for many of them is public housing. But local housing authorities across the country write their own rules. And they routinely bar applicants with criminal convictions — and often people with mere arrest records. That means these policies can affect the nearly one in three Americans who have some kind of criminal record.

Some people are excluded by federal law, specifically certain sex offenders and people who have been convicted of making methamphetamine in public housing. Otherwise, administrators from the nation’s 3,300 public housing authorities, which serve 1.2 million households, are supposed to balance family unity against a person’s potential risk to society as they consider applications. But far too often, they divide families without cause.

A single arrest in the past five years, for instance, can jeopardize a family’s application to public housing in parts of Maine, Pennsylvania, Georgia, Oklahoma and California. In St. Louis, anyone who has used, sold or made drugs in the past decade is barred from public housing.