A woman posing as a health visitor has made a second attempt to trick her way into a family's home to see a young child.
The woman called at the home of a family in Faringdon and detectives believe she was the same woman who made a similar failed attempt in the town.
They fear she may be sexually motivated or want to take pictures of children.
Detectives have warned parents to call 999 immediately if they are approached.
The woman called at a house in Eaton Close on Friday, claiming to be a health visitor and saying she needed to check on one of the children, whom she knew by name. The child's mother asked why her normal health visitor had not come and sent the woman away, explaining she was too busy. When she called to arrange an appointment, the White Horse Health Centre told her no-one had been sent to her home.
In a similar incident on May 22, a woman called at a house in Lansdown Road.
Det Sgt Chris Biddle said: "On neither occasion has she been able to get near any of the children. But as yet, we do not know why she's doing this. It may be sexual or to take photographs, but it's unlikely at this stage to be an attempt to snatch a child, because that rarely happens when parents are around."
The woman is aged about 30, 5ft 7in tall, of medium build, with fair hair in a bob style.
An Oxfordshire NHS Primary Care Trust spokesman said: "Health visitors arrange in advance to visit a client at home. If a client or patient is visited by an individual they do not know, they should always ask for identification. If in doubt, they should not let the person in."
Anyone visited from a bogus health visitor should call 999 immediately.
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