A man was seen acting suspiciously near the Melbourne house where a mother of three was found dead by her twin daughters.
Kylie Blackwood was killed at her Pakenham home sometime between midday and 3.40pm (AEST) on Thursday, police say.
Detective Inspector John Potter said Mrs Blackwood was the victim of a vicious assault.
He said a tradesman working on a nearby house saw a man dressed in dark clothing peering into other homes in the street.
The man may have been casing homes to rob, Det Insp Potter said.
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"This man was seen by the tradesman around midday, which is the same time we believe Mrs Blackwood returned to her home," he told reporters on Monday.
"It's possible this man may not have been involved, but we need to talk to this man and find out what he was doing in the street."
Det Insp Potter said the man may have gained access to the McCaffrey Rise house via the garage, which was left open.
Police are examining other recent daytime burglaries in the area.
Det Insp Potter said police have yet to find a murder weapon or identify any missing items, as the distraught family has not returned to the premises.
The 42-year-old was found by her 11-year-old twin daughters when they returned home from school.
Police say the twins, who have a 13-year-old brother, were extremely traumatised by what they saw.
The man they are seeking was wearing a grey-striped hooded top, dark trousers, a black cap and sunglasses.
