The bodies of Kyle Devine, who was 27, 24-year-old Clarissa English and her 18-year-old brother, Dakota English, were found Tuesday in their Lethbridge townhouse.
A concerned neighbour had called police to check on the residents.
Facebook profiles under their names suggest Devine and the woman were in a romantic relationship.
Officers have described the crime scene as violent, but have not released how the three died.
Police say it was not a random crime and there is no risk to the public.