State Representative Melissa Hortman and her husband, Mark, were both shot dead in their home in Brooklyn Park, a city north of Minneapolis, on Saturday morning. John A. Hoffman, a Democratic state senator, and his wife, Yvette, were also shot in their home, located not far from the Hortmans’ residence. Both survived.

Police have been searching for Vance Luther Boelter, the suspect in the shooting of two Democratic state politicians from Minnesota.

When the gunman in the shootings of two Minnesota lawmakers approached their homes early on Saturday morning, he was armed with not just a handgun but also a wealth of other gear: a black tactical vest, a badge, a flashlight, a Taser. He arrived in a black S.U.V. with flashing police lights.