CHICAGO – Authorities said Tuesday they are investigating whether the shooting deaths of a federal judge’s husband and her frail, 89-year-old mother were the work of white supremacists out for revenge.

The killings came a month before white supremacist Matt Hale was scheduled to be sentenced for trying to have the judge, Joan Humphrey Lefkow, killed over her handling of a trademark dispute involving his hate group.

Police said they were looking at the possibility the crime was committed by hate groups but cautioned that it was “but one facet of our investigation.” Still, from the federal courthouse to the family’s neighborhood, the talk was about Lefkow’s involvement in the white supremacist case.

“There is much speculation about possible links between this crime and the possible involvement of hate groups. We are looking in many, many directions, but it would be far too early to draw any definitive links,” said James Molloy, Chicago’s chief of detectives.

The judge and other members of her family were placed under federal protection after the killings.

On Monday, the judge came home to discover the bodies of her husband, Michael F. Lefkow, 64, a lawyer, and her mother, Donna Humphrey, in the basement of the Lefkows’ North Side house.

A federal source who spoke on condition of anonymity said the victims had been shot in the head. Another source said that police found two .22-caliber casings and that a window at the house had been broken.

The two victims would have been easy to overpower. Lefkow family friend Thomas Robb described them as “very vulnerable people,” explaining that Humphrey, who was visiting from Denver, needed two canes to walk. Michael Lefkow had undergone surgery last week to repair a ruptured Achilles tendon and was on crutches, he said.

“All of us are horrified by the murder of Judge Lefkow’s husband and mother. Nothing can prepare us for such a stunning, tragic event,” said Charles P. Kocoras, chief federal judge for the Northern District of Illinois.