North Down MP Lady Sylvia Hermon has called on the secretary of state to clarify what would happen to border security with the Republic of Ireland if the UK leaves the European Union.
Lady Hermon said Theresa Villiers must state what steps she would put in place in the event of a Brexit.
The independent MP said Ms Villiers has a responsibility to explain "precisely what is going to happen to the border".
She questioned how the PSNI could police border checks.
Insisting that she was "not scaremongering", Lady Hermon said: "I live here, I am going to continue to live here. I love Northern Ireland. I am a unionist.
"I want to know from our Secretary of State what she anticipates are going to be the arrangements along the border with the Republic of Ireland in the event of the UK voting to come out of the EU."
In response, Ms Villiers, who is in the Leave campaign, told the BBC that fears about border security were wrong.
She said: "It really is a scare story to say that suddenly we are going to have Troubles-style security checks and towers around the border.
"It is not going to happen. We can keep an open border with the Republic of Ireland."
The cabinet minister added: "The Common Travel Area has survived a civil war, a world war and 30 years of the Troubles. Of course it is going to survive a Brexit vote."
Lady Hermon also has concerns about the future of the UK if voters back a move to leave the EU.
"In the event of a Brexit, Alex Salmond estimated that within two years, there would be another independence referendum in Scotland," she said.
"I am a unionist. I do not want to accelerate the break up of the United Kingdom. Of course I am deeply worried."
However, Ms Villiers does not believe that the make-up of the UK is under threat if voters back a Brexit.
She told the BBC: "When the Scots voted to stay in the United Kingdom, they knew perfectly well that there was a forthcoming referendum on EU membership, in which the United Kingdom would vote as a whole.
"So a Brexit vote does not change this situation in Scotland. The matters relating to Scottish separation from the UK have been settled by that Scottish referendum and its decisive vote to stay in."
On Thursday, two former prime ministers - Sir John Major and Tony Blair - visited Northern Ireland to warn of the dangers of leaving the European Union.
They said an exit could undermine the peace process in Northern Ireland and encouraged voters to back a move to keep the UK in the EU.
The First Minister, Arlene Foster, said she found the intervention by Tony Blair and Sir John Major "rather sad".
She told journalists: "I do find it rather disgraceful for two prime ministers, who know full well the importance of the peace process here in Northern Ireland, to come over here and suggest that a vote in a particular direction is going to undermine that, is quite scandalous."
You can hear interviews with Lady Hermon and Theresa Villiers on Inside Politics on BBC Radio Ulster at 18.00 hours on Friday and repeated on Saturday at 13.35.