In his ruling Tuesday, Ontario court judge Philip Downes criticized the Crown for attempting to string out the process.
"In my view, the Crown's position is unjustified and unreasonable," Downes said in his decision.
"The Crown's position is not compatible with the presumption that judicial proceedings are open and public."
Several media outlets are asking the courts to let them see the documents as a matter of "great public interest" given the possible link to the mayor.
At the very least, the media lawyers argued they should be given the materials in confidence so they can make informed arguments as to why the documents should be made public.
The Crown said it needed at least six months to do that.
Instead, Downes ordered the Crown to turn over the 205 pages in confidence to the lawyers by Aug. 27 to allow them to prepare arguments on why the warrants should be public.
The judge did say the Crown could black out parts it deems too sensitive for release pending the full hearing, which he hoped would occur by mid-September.
Lawyer Peter Jacobsen, who is acting for the media outlets including The Canadian Press, the Star, the Globe and Mail, CBC, CTV and Postmedia, said he was pleased with the ruling.
"We were absolutely successful in getting a process put into place," Jacobsen said.
"The Crown has now been put to the requirement of getting us the documents by Aug. 27, and that to me is a good result."
In late May, police raided 12 addresses in northwestern Toronto as part of "Project Traveller," an investigation into gang activity. Police arrested more than 40 people and, among other things, seized firearms, drugs and cash during the raids.
"There are reports that the residential complex along Dixon Road at the heart of the raids includes a location where the alleged video depicting Mayor Ford may have been kept," the media application to Downes stated.
"This matter is of great public interest as it may relate to allegations that the mayor of Toronto has been associated with members of a criminal organization and was videotaped by them using crack cocaine."
Earlier in May, the American website Gawker and the Toronto Star reported seeing a cellphone video apparently taken by a drug dealer showing Ford appearing to smoke crack cocaine. They also published a photograph of the mayor with three men, one of whom was gunned down on a city street.
The other two men were arrested as part of "Project Traveller."
Ford has said he does not use crack and is not a crack addict. He has also said the alleged video does not exist.
The Star later reported that Ford had told senior aides he knew where the video was. The alleged video has never surfaced, even though Gawker raised $200,000 to try to buy it.
Last month, CTV News reported police apparently had heard of the alleged video weeks before the Gawker and Star reports.
Jacobsen said he was also pleased Downes had taken his concerns seriously about the difficulties in obtaining court documents.
"I do not see why there should be any resistance to providing the material," Downes said in his decision.
However, Downes said he was unsure he had the authority at this stage to make a blanket order as to how court offices should deal with media access requests.
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