Police received an allegation that a woman attempted to take a two-year-old child from the arms of a mother on Harry Mitchell Park, Smethwick at around 7.40am on Thursday 14 April.
Officers arrived in the area within minutes and have launched an investigation.
Since the call, officers having being liaising with nearby schools, dog walkers and local residents to see if this woman can be identified.
Extra officers have also been brought in to patrol the area at key times.
The woman is described as dark skinned in her mid 20s and around 5ft 8ins tall.
She was wearing a long light coloured ankle-length skirt and a light jacket.
She had her hair pulled up and covered in a dark headscarf or bandana and was wearing hoop earrings.
She spoke with an accent.
DI Colin Mattinson, from Smethwick CID, said: “We continue to appeal for information and would ask anyone...
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