A city criminal-diversion program can be sued over a stabbing committed by one of its rehab patients, a state appeals court ruled Thursday.

The patient, Sean Velentzas, 33, was sent to the Queens Village Committee for Mental Health after robbing a cabdriver at gunpoint in 2010 — and not to prison despite his criminal history, records show.

Weeks into the program, a drunken and “enraged” Velentzas shoved a fellow patient, the ruling said.

When staff called cops, Velentzas was escorted off the property and ended up at his grandmother’s home, where he stabbed his mom’s boyfriend.

The boyfriend, Anthony Oddo, 58, sued the facility, claiming it had a ­legal duty not to release Velentzas.

“When the going got tough in controlling this violent man, Queens Village washed its hands with terrible consequences,” said Seth Harris, Oddo’s attorney.

Alternative sentencing has come under new scrutiny since October, when NYPD Officer Randolph Holder was slain allegedly by Tyrone Howard, a gangbanger sent to rehab instead of prison.