A legal loophole that means coronavirus lockdown regulations are not applicable to day-trippers from Northern Ireland while in the Republic does not apply the other way around.
Garda headquarters in Dublin has told officers that Covid-19 restrictions do not affect visitors from over the border.
Officers have been ordered not to arrest anyone from Northern Ireland for suspected breaches of the Republic's coronavirus regulations because the emergency legislation only applies to people resident in the state.
However, Alliance MLA John Blair has since asked the chair of the Policing Board to question Chief Constable Simon Byrne over whether day-trippers from here who have clearly been caught making a non-essential journey over the frontier can be prosecuted if their details are passed to the PSNI by the Garda.
Assistant Chief Constable Alan Todd said that the Republic's Covid-19 regulations are not the same as those that apply here.
"The form of words in terms of relevant geographical location do not apply to the Northern Ireland regulations," he added.
Policing Board member and South Antrim MLA Mr Blair stated that the issue of people travelling across the border on day trips is an "area of concern" and said he will put the question to Mr Byrne through the board.
"The travel restrictions which were clearly laid out a few weeks ago remain in place and they are there in the interests of stopping the spread of coronavirus and saving lives," he said.
However, TUV leader Jim Allister said it would become "very burdensome" for the PSNI if they attempted to prosecute people who had been caught by the Garda on a day trip across the border.
"I think it would be tricky enough because how do the PSNI prove that?" he said.
"It would become an elaborate weave of evidence to prove why someone was south of the border and that they were stopped.
"All of those things would be essential proofs and it would become very burdensome to prove all of that."
Health Minster Robin Swann also expressed concerns yesterday that people were beginning to become complacent in the fight against Covid-19.
He said there would be no timetable as to when we will begin to exit the lockdown strategy.
"I think it will encourage a greater sense of ease and complacency if people think: 'Well, if it'll be all right in two weeks so it'll be all right today'," he told the BBC.
Writing in today's Belfast Telegraph, Minister for the Cabinet Office in Westminster Michael Gove said that it is "entirely understandable" that people want to know if an end to the lockdown is in sight, but admitted the disease will be here "for some time".
"Tragically, 299 people in Northern Ireland have lost their lives to this invisible killer, and it is thanks to all your efforts that the figure is not higher still," said the Conservative MP.
"Only once we are reassured on our five key tests can we safely adjust the distancing regime: the NHS's ability to cope; a sustained fall in daily death rates; reliable scientific data showing the infection rate falling to manageable levels; sufficient testing capacity, and PPE to meet future demand."
Elsewhere, Foreign Secretary Dominic Raab has dismissed calls for an early easing of the lockdown.
He said the outbreak was still at a "delicate and dangerous" stage.
He added: "We need to make sure that the next steps are sure-footed, which is why we are proceeding very cautiously and we are sticking to the scientific advice."