The party says it has passed apparent video evidence on to gardaí
Labour says they will consider pressing charges against people taking down their referendum posters.
The party believes there has been a concerted effort to remove their Vote Yes posters, claiming it's happening 'across the country'.
Jan O'Sullivan TD has passed video evidence of an apparent incident in Limerick on to gardaí.
Labour leader Brendan Howlin acknowledged: "The law is actually not all that clear about it. There is no specific law other than they are the private property of the Labour party, that we're entitled to put up during a referendum campaign.
"It would be a matter of theft, actually, would be the offence being committed."
He argued: "In terms of any fair running of a vote of the people, it has always been understood across the party political system that people are entitled to put up their posters without later hindrance. The notion that there would be any campaign to remove them is unacceptable."
Labour also claims some illegal No posters are being erected which do not say who paid for them, which is against the law.
Deputy Howlin observed: "We don't know who is responsible for them on the No side, and that of course is clearly illegal.
"It is an offence under the Electoral Act, and I think that's something that should be pursued."
Reporting by Sean Defoe and Stephen McNeice