Three women police officers spent a day in full Muslim dress as part of a scheme to improve community understanding.
Two sergeants and a community support officer dressed in head-to-foot burkhas and other traditional clothing and went out shopping.
Meanwhile a group of Muslim women were invited into police cells, a CCTV control room and shown other daily duties of a police officer.
The move was part of a police initiative dubbed "In Your Shoes" taking place in Sheffield, South Yorkshire.
But it has attracted strong criticism from onlookers.
Matthew Elliott, of the Taxpayers' Alliance, said: "This is an absurd diversion from real policing.
"People want the police out catching criminals, not indulging in Politically Correct gimmicks.
"The police are overstretched as it is without officers being paid to do other things than their real job."
Douglas Murray, director of the Centre for Social Cohesion, said: "This has nothing to do with crime.
"Like most people who have been a victim of crime, I am amazed and flabbergasted that they have solved all the crimes so they can spend a day playing dressing-up games.
"I did not know it was the job of police to see how people feel. I thought it was their job to solve crimes.
"This is a fantastic demonstration that for the last 10 years the British police have been having an institutional nervous breakdown. They do not know what their job or their role is."
The clothes-swapping day took place earlier this year in Sheffield town centre and followed a similar event in Barnsley.
The officers wore brightly-coloured traditional Muslim outfits and a full-length black jilbab plus a niqab, which covers the face leaving slits for eyes.
Sergeant Deb Leonard, who wore some of the clothing, described her experience in a South Yorkshire Police in-house magazine.
She said: "I have gained an appreciation and understanding of what Muslim females experience when they walk out in public in clothing appropriate to their beliefs.
"We are keen to gain a better understanding of issues which our communities face."
No one from South Yorkshire Police was available to comment.
But the in-house magazine added: "The exercise is just one of many activities South Yorkshire Police has planned with communities and ethnic minority leaders to secure strong relationships, celebrate diversity and encourage integration, working towards a safer, closer society."Reuse content