A superior court in Connecticut granted a sweeping victory to the families of eight people killed in a 2012 mass shooting at Sandy Hook Elementary School in Newtown, Conn., suing the far-right broadcaster and conspiracy theorist Alex Jones and his Infowars media outlet for defamation.

The judge in Connecticut ruled on Monday that because Mr. Jones refused to turn over documents ordered by the courts, including financial records, he was liable by default. The ruling combines with three previous rulings in Texas to grant the families of 10 Sandy Hook shooting victims four victories in four defamation lawsuits against Mr. Jones.

Mr. Jones for years spread bogus theories that the shooting that killed 20 first graders and six educators was a government-led plot to confiscate Americans’ firearms and that the victims’ families were “actors” in the scheme.

The Sandy Hook families maintain that Mr. Jones profited from spreading lies about their relatives’ murders. Mr. Jones has disputed that, while for years failing to produce sufficient records to bolster his claims.

Juries in both states will next decide how much Mr. Jones should pay the families in damages, atop court costs. Those trials are scheduled for next year in both states.

This is a developing story. Check back for updates.