According to Mr Coulibaly, his four-year-old daughter Adjaratou was abducted from in front of his house in September last year.
Four months later, in January this year, Adjaratou was spotted by a friend. She was with a German couple in central Bamako.
The Germans had legally adopted Adjaratou and were due to fly with her to Germany in a couple of days.
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The head of the orphanage Adjaratou was adopted from, Pona Hawa Camara, says the child was brought to her by a woman one evening and she reported the arrival to the police.
"The woman said that she'd had the girl for a week and that she'd taken the child from door to door and even to the head of the neighbourhood, and that no-one recognised her."
The head of the police department in Mali which deals with such cases, Ami Kane, says, however, that Adjaratou's arrival was never reported to them.
Many families accuse the police of not taking the cases of missing children seriously Ms Camara said she would give the BBC the date the child arrived at her orphanage and the name of the person who handed her over.
She now refuses to do this or to answer any more questions.
The German organisation that assisted in organising the adoption, Help A Child, refused to make a statement about the case.
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