The PSNI has not fined a single person who has failed to wear a face mask in a shop - one week after the controversial rule was introduced.
Retailers and staff insisted last week that they were not responsible for enforcing the regulation, which came into force last Monday, while the PSNI said it would "only use enforcement as a last resort".
Policing Board member Mervyn Storey felt that the public wants to see the rule enforced but it is unclear as to who should be taking the lead.
Prior to the rule's introduction, the Department of Health said it was expected that businesses would help encourage compliance.
However, responsibility for imposing possible fines of £60 for non-compliance rests with the PSNI.
Executive guidance also warned shoppers not to challenge anyone who fails to cover up.
The PSNI said refusing to wear a mask was not an arrestable offence, and that it would instead "engage, explain and encourage people to make the right choices and this includes the mandatory wearing of face coverings", while enforcement "will be a last resort".
It stressed that "primary responsibility for ensuring compliance" lies with businesses.
The PSNI confirmed yesterday that no one has been fined for flouting the regulation but declined to comment further.
DUP MLA Mr Storey felt that the PSNI was trying to be "pragmatic" in its stance over enforcement.
"Shopkeepers don't want to have the responsibility to be the individuals who are seen to be enforcing this or demanding that this is the case," he said.
"The police are trying to - as they have done in the past - take a position of encouraging people to abide by this.
"Unfortunately, we get ourselves into the position where it could end up in the courts because someone could challenge the particular fine in relation to this.
"You then have to ask if there is enough evidence and is it in the public interest.
"Those are the two criteria that will determine any issue that would go to court."
Meanwhile, SDLP Assembly member Daniel McCrossan criticised those responsible for painting anti-face mask graffiti on a wall in Strabane, telling them to "wise up".
The graffiti stated: "No new normal #NoMaskTyranny #KBF [Keep Britain Free]."
Posting a picture of the graffiti, Mr McCrossan said that while he supports anyone's right to protest, he cannot support "mindless vandalism of public property which blights our town".
"Whoever did this - wise up," continued the West Tyrone MLA.
"Protest if you like but don't vandalise or blight our town.
"I'm sure the person(s) responsible wouldn't want this sprayed across the front of their house.
"Masks are there to help prevent the spread of the virus.
"As for the KBF hashtag - I'll say nothing."