Fairfax Media can reveal search warrants used to raid the Construction, Forestry, Mining and Electrical Union ACT branch headquarters last month named secretary, Mr Hall, as a suspect in the blackmail of Canberra builder, Dennis Milin.

Former CFMEU organiser Halafihi "Fihi" Kivalu and serving official John Lomax – who have both been charged by police with blackmail – were also named on the warrant.

About 20 police, acting on evidence gathered through the Trade Union Royal Commission, raided the Dickson office on August 26, staying for about 13 hours and seizing about 10,000 electronic and hard copy files.

The police have subsequently volunteered to not access or examine seized materials – effectively halting part of the probe – until a court can rule on the lawfulness of the search and confiscation.

A copy of the warrant, filed as part of the CFMEU lawsuit to have the material returned or destroyed, said police suspected the raid would uncover evidence that Mr Hall had blackmailed Mr Milin, director of Milin Builders, between March and April 2012, and in August 2014.

While the basis for police suspicions are unknown, Mr Milin told the TURC in July that Mr Hall had, in 2014, threatened that Milin Builders would not be able to participate in a $75 million apartment project in Woden without a union enterprise agreement.

Mr Milin also said his firm was kicked off a $90 million residential tower-block development in 2012 because Mr Hall wanted contractors to have union EBAs and memberships.

ACT Policing said investigations continued, but "it would be inappropriate for ACT Policing to make any further comment whilst this matter is still in the investigation stage."

Mr Hall, who has not been charged with any offences, said the allegations had been another attempt by the Coalition Government to criminalise the work of unions.

"Criminalising the work of unions to get better conditions and safety for workers is a fundamental attack on people's rights to have decent pay and conditions," he said.

"This should be a concern for every single worker in Australia.

"I go to work everyday and try to improve the life of building and construction workers, I'm very proud of what I do and won't be intimidated by the police."

Mr Hall is not the only CFMEU boss to be scrutinised by police attached to the TURC.

Last month, Fairfax Media revealed police in three states were honing in the most senior leaders of the CFMEU for allegations ranging from receiving secret commissions to blackmail.

In Victoria, police taskforce, Heracles, has taken witness statements from construction industry figures as detectives attempt to charge Victorian CFMEU secretary John Setka and his deputy, Shaun Reardon, with blackmail in connection to the union's campaign against concrete firm Boral.

The CFMEU's NSW secretary Brian Parker is also being investigated by police after phone taps were recently aired at the union royal commission, which revealed his close relationship with organised crime figure, and allegedly crooked labour hire firm boss, George Alex.