Australian police are considering using fingerprints to identify people wearing face-covering veils, after a judge said he could not be sure a burqa-clad woman was who she told police she was.

The judge said this week that a case against Carnita Matthews, who a magistrate earlier found had made a false complaint against police, could not be upheld partly because he could not be sure she had made the complaint.

The complaint was made by a burqa-wearing woman to a Sydney police station but officers never saw the woman's face.

"I am not satisfied beyond reasonable doubt that she made the complaint," Judge Clive Jeffreys said on Monday.

Following the decision, New South Wales state Police Minister Mike Gallacher said he would ask police to consider improved identification strategies for those wearing items such as the burqa -- which covers a woman's head and body.

One such strategy could be that "where the person elects not to remove their facial covering that they can provide a fingerprint as a means of identification", he told ABC television.

Gallacher said it was possible that fingerprints could be included on statutory declarations and other statements to ensure they were authentic.

The New South Wales government said regardless of religion or gender, all people were required to obey the law.

"Whether you're wearing a clown's mask, whether you're wearing a motorcycle helmet, whether you're wearing a face veil of any form, police can and have the power to demand that you remove it," Premier Barry O'Farrell said.