Northern Ireland's largest trade union, Nipsa, is to recommend to its members that they should vote for the UK to leave the EU.
The Northern Ireland Public Service Alliance has about 45,000 members working across the public sector.
On Friday, delegates to the union's conference voted in favour of a pro-Brexit motion by 68 votes to 58.
But the trade union umbrella group, the Irish Congress of Trade Unions (ICTU), wants the UK to remain in the EU.
In April, delegates to the ICTU'S Northern Ireland Committee conference overwhelming passed a motion of opposition to a British exit (Brexit) from the European Union.
The committee called on workers to vote to remain "for the stability of the economy of Northern Ireland, for the security of their jobs and for their rights as workers".
The UK's largest trade unions - Unite, the GMB and Unison - are all in favour of remaining in the EU.
The RMT transport union is in favour of leaving.
The motion debated by Nipsa members on Friday described the EU as "a club for the rich" that does not provide "meaningful assistance to workers".