Brooklyn Park police officers arrived just in time to see Boelter shoot Mark Hortman through the open door of the home and exchanged gunfire with Boelter, who fled into the home before escaping, the complaint said. Melissa Hortman was found dead inside, according to the document.
Authorities said Boelter posed as a police officer, even allegedly altering a vehicle to make it look like a police car.
A Minnesota lawmaker said Hortman's dog had to be euthanized after being shot in the attack.
Authorities didn't give a motive for the shootings as they announced Boelter's arrest.