Toni McNelis, 24, and her five month old daughter have gone missing from an address in Marine Drive in the north of the Capital.
The pair were last seen leaving the area on the evening of Wednesday 21 February.
Toni is described as being of average build with long brown hair and brown eyes.
Inspector Graeme Dignan said “Concerns are growing for the welfare of Toni and her daughter and we area appealing to anyone who may have seen them recently, or know of their whereabouts to get in touch with us through the 101 number.
“This is out of character for Toni and I would ask anyone who may have seen them to call us immediately in so we can ensure she is safe and well.
“Likewise I would ask Toni herself to get in touch with us if she sees this appeal in order to let us know she is safe and well.”
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