The Stormont minister for education has been challenged to publish the findings of a survey which was delivered to thousands of parents in the Dungannon District.
The questionnaire aimed to gauge the level of demand among local parents in securing a place for their child across the border.
Parents who lived within 12 miles of the border were asked for their views.
The results were expected to be released at a North-South Ministerial Council meeting in February 2013, but that did not happen.
O’Dowd said the council must first consider the survey and authorise publication.
Figures from the Departments of Education, north and south, show that 275 children from the border counties in the Republic of Ireland travel to secondary schools in Northern Ireland.
However, only a quarter of that number travel from Northern Ireland to schools in the Republic of Ireland.
Most of those who cross the border are secondary school pupils, but 132 primary school pupils also travel to the north from the south.
The DUP’s education spokesman Mervyn Storey said there is a high cost to the Department of Education in Northern Ireland and he wants to know if the Republic of Ireland’s government is being paid for teaching the pupils who cross the border for their education.
The Department of Education in Dublin said no money changes hands because EU rules entitle children from one region to free education in another.
Mr Storey said he believed the survey was being suppressed because it did not show the results that Mr O’Dowd was expecting.
“I think he was probably expecting there was a migration of pupils from Northern Ireland to the Republic, the reverse is clearly the case,” he said.
The reasons parents gave for travelling to Northern Ireland ranged from geographical convenience to their view that the system in Northern Ireland was better and that children with learning difficulties got more support.
Mr Storey, who is also the chair of the assembly’s education committee, said he had no objection to the cross border traffic to schools.
“My question to the minister is, how much is that costing the Northern Ireland taxpayer and how is that being funded by the educational system in the Republic,” he said.
“I need to be content the money is being spent in a way which is benefit to children in Northern Ireland and not just a free service for anyone who wants to use it.”