The Danish police complaints department said on Wednesday that police were investigating a veiled protester during a demonstration in Copenhagen against the ban on face coverings.
A Reuters photographer took pictures of the August 1 incident in what appeared to be the protestor crying when the ban on face cover came into effect in public places nationwide.
"The picture has made the police involuntarily acting in a very sensitive political debate where they should have participated," said Marcos Knut, a parliamentarian from the Liberal Party, the largest party in the government.
Hu and others drew the attention of the independent complaints panel to the incident. "The police mission is to enforce the law and not embrace those who oppose it," he said.
Turbine Koch, the police lawyer, said she felt she had been proportionately treated in her role as a "dialogue cop," a specialty created to ease tensions during demonstrations.
"This is nonsense," said Koch. "As my client said, if anyone else was in the same position to do the same thing, then it has nothing to do with wearing the niqab."
The ban has exposed deep divisions within Danish society; some argue that it supports secular and democratic values, while others say it infringes freedoms, such as faith and expression.
France, Belgium, the Netherlands, Bulgaria and the Bavarian state of Germany imposed restrictions on full-face coverings in public places.