The two briefly exchanged words at the front door before the man fired the crossbow, hitting the woman with an arrow that caused life-threatening injuries.
"This was most definitely a targeted type of attack", Peel Police Detective Sgt. Jim Kettles told reporters at a press conference on Monday, April 15.
Police said the crossbow was never removed from the box during the attack.
Police called the incident, which was caught on surveillance camera, a "premeditated, targeted, and isolated attack".
"Comments that were made to the victim by the suspect indicate that the victim was targeted", Supt.
Police are also searching for information on a dark-coloured pickup truck that may have been used as a getaway vehicle, arriving in the neighbourhood minutes before and fleeing minutes after the attack.
Police appear to have edited the video to avoid showing the exact moment when the crossbow was sacked.
The woman is not expected to make a full recovery.
"The injuries that she sustained were absolutely devastating", Kettles said, adding that the weapon used by the suspect was a crossbow that could be used to take down big game like moose.
The attack - being investigated as an attempted murder - was carried out in the city of Ontario in Canada last November. "This is something we are attempting to establish".
As for the victim, she survived but Kettles said she suffered severe damage to multiple internal organs. "I can't speak to those at this time", Kettles said.
"The suspect may have attended with another individual", he said. "The face on its own, although that may not trigger anything, perhaps in conjunction with the cap that he's wearing and the shoes he's got on - that may mean something to somebody", Kettles said.
In the meantime, police are appealing to the public for help identifying the suspect, adding that aside from wearing a baseball cap, he did not hide his face.
"Anybody over the age of 18 can purchase one of these weapons at any sporting-goods store that happen to carry them", Det.
The day following the attack, forensic investigators searched the house and collected evidence including an arrow believed to have injured the woman as well as surveillance footage of the suspect and incident.
If you know anything, contact Peel regional police or Crime Stoppers.