"That is also believed to be why the man came to the address on Christmas Day," the police write on their website.
The motive behind the murder of the woman, who was in her mid-50s, is still unknown.
The suspected perpetrator - who called and was let into the villa at 8:30 a.m. on Christmas Day - was shot dead when police arrived shortly after 12 p.m., after police had been summoned from inside the home.
The woman's teenage daughters were also subjected to violence. One of them is still being treated at a hospital but is said to be in a stable condition.
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