Police are following up "positive lines of inquiry" over an incident where a Hamilton woman was sexually assaulted as she slept in her home.

Detective Senior Sergeant Mark Greene, of the Hamilton CIB, said a man entered the woman's home about 1.45am on Saturday.

The intruder, who is not believed to be known to the woman, then sexually assaulted the woman as she slept in her bed.

He then fled from the house, which is on a street south of the Dinsdale shopping centre towards Templeview.

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When contacted today, Greene said they had received several leads after a public appeal for information on Monday.

"We've got some good responses from the public post we had ... we're following up some positive lines of inquiry."

He said there wasn't a lot of extra detail to divulge to the public yet but they hoped to obtain CCTV footage from in and around the area to help their investigation.

"We possibly could have some CCTV footage, we're still working on that, for the area in and around where the offence happened, not from the scene itself."

At the time of incident, police sent a dog unit but were unable to find the man.

The offender was described as wearing a white or tan-coloured T-shirt, about 1.8m tall, with wide shoulders, and wearing a beanie and may possibly have had a bicycle.

Greene said it had been a frightening experience for the victim who was being supported by police.

Anyone who may have seen anything or anyone unusual in the Dinsdale area in the early hours of Saturday, or has information which could help, is asked to contact Hamilton Police on (07) 858 6200.