The 48-hour leave was his 14th after serving several prison sentences for theft and drug dealing since 2003, according to The New York Times.
So if this was terrorism inspired by ISIS, the question turns to when and where Herman became radicalized. She was released when police shot the 36-year-old attacker dead.
The Belgian prime minister, Charles Michel, said Herman had been indirectly mentioned in state security reports on radicalisation but he was not on a watchlist.
Herman attacked two female police officers from behind with a knife, stabbing them repeatedly, before stealing their handguns and shooting them as they lay on the ground.
Belgian media have identified the suspect in Tuesday's attack as Benjamin Herman, a Belgian national born in 1982, though in keeping with standard procedure authorities declined to confirm his identity.
The number of police officers and armed soldiers patrolling the streets of major cities has crept up in Belgium and several other European countries, and officers have been killed or wounded on such patrols in several attacks over the past three years.
Herman reportedly approached two female officers Tuesday, stabbed them and then took their guns and shot them.
He then seized a firearm from one of the policewomen and shot them both dead, as well as a passenger in a nearby auto.
The woman he took hostage might have talked the shooter down and helped to avoid more deaths inside the school, he added.
He then shot dead a 22-year-old man who happened to be in the area, before taking a woman hostage.
A senior official at the prosecutor's office told reporters "there are indications it could be a terror attack".
"They reacted well. All the systems, all the procedures worked, but if you are attacked from behind, as was the case with the two officers, you can't do anything", he said.
Despite the potential terrorism link, Belgium's crisis centre said it saw no reason to raise the country's terror threat alert for now.
"There is absolutely no confirmation yet that the incident is terror-related", Stevens told the AP.
On Tuesday in Liege, Belgium the two cops were slaughtered together by a violent knife-wielding thug.