The challenge was brought by victims campaigner, Raymond McCord
A case at Belfast High Court opposing Prime Minister Theresa May's ability to trigger Brexit negotiations by next March was taken by a cross-community group of politicians and human rights campaigners.
They want to establish that devolved decision-makers at the Stormont Assembly can veto Brexit, assert rights to consultation over whether to launch talks with Europe and protect peace process guarantees enshrined in the 1998 Good Friday Agreement which largely ended republican and loyalist violence.
Raymond McCord, whose son Raymond McCord Jr was murdered by the loyalist Ulster Volunteer Force (UVF) in north Belfast in 1997, is a party to the case who has concerns that European peace money which goes towards victims of the Troubles may be discontinued following an exit.
During several days of hearings recently a lawyer for Mr McCord argued that Northern Ireland could block withdrawal from the EU.
The barrister said the country enjoyed control over its own constitutional change including all-island relations following the 1998 Agreement.
Northern Ireland shares the UK's only land border with an EU state, the Republic of Ireland, and the British and Irish Governments have said they are keen to ensure there is no return to the hard borders of the past.
If the UK leaves the customs union, the EU could demand a secure frontier in Ireland to prevent goods flowing in and out of the EU from Northern Ireland without paying required tariffs or facing checks on rules of origin.
Stormont's senior legal adviser attorney general John Larkin told the court nothing in the Belfast Agreement which largely ended violence in 1998 had been affected by Brexit.
He said there were no substantive obligations in the Agreement which required continued membership of the EU.
A barrister for the UK Government said no court could block the will of the people as expressed in the June referendum.
Some 56% of Northern Irish voters backed Remain but some unionist-dominated areas supported Leave. The largest party in Northern Ireland, the Democratic Unionists, campaigned for an exit.
Former Stormont justice minister David Ford, senior Sinn Fein Assembly member John O'Dowd and nationalist SDLP leader Colum Eastwood are among those supporting the challenge.
In London, an investment manager and hairdresser are taking legal action opposing the right of the Government to start the process of withdrawing the UK from the EU without a vote in Parliament.