The mugging happened on Sunday evening around 6:30 p.m. in Noe Valley near Sanchez and 28th street.
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According to police, a 37-year-old woman had left a friend's home in the vicinity with her 6-month-old baby.
She told investigators she didn't remember much, except that a stranger approached her from behind, striking her in the head.
The woman fell to the ground, fracturing her skull.
Public Information Officer Joseph Tomlinson tells ABC7 News she went through surgery and is listed in "life threatening condition."
Fortunately, her baby did not suffer injuries.
Police responded but didn't find the assailant.
They're looking for security video and are appealing for help from the public.
On Noe Valley's "Next Door" internet site, someone posted information, saying a neighbor reported seeing a man in his 20s or 30s wearing a "black backpack" hanging out near a house on 27th street about a block away from the crime scene, for about 30 minutes, watching people walk by.
If you have information, please call SFPD.