A 38-year-old woman was assaulted by an unknown person as she walked along Safety Bay Road near Wilson Park at 12.30am.

She received serious head injuries and was taken to Rockingham Hospital and then Royal Perth Hospital, where she was in a stable condition on Friday at 10am.

Radio 6PR reporter Michael Stamp said police on Friday morning had tapered off an area for forensic investigation after finding a number of blood stains.

"There's blood stains across the footpath outside the library and then across the road we've got more blood stains along that footpath and on the grass," he said.

"A house across the road has blood stains across the front door near the door bell, so we're guessing the woman tried to get these people's attention - it's an elderly couple that live at the home.

"It's dry now but has dripped down the door onto the wall and there are a few blood stains on the floor as well."

Police would like to speak to anyone who was in the area between 11pm and 12.30am who saw any suspicious person/s, vehicles or activity.

The woman attacked is described as being fair skinned with a slim build and brown hair.

She was wearing a dark-coloured jumper, white pants and bright pink running shoes.

Anyone with information is asked to call Crime Stoppers on 1800 333 000