Ayers and other city officials have said a collapse zone was properly established. Neary and Sweeney were killed when one of the building's five-story brick walls fell on an adjacent furniture store, where they were performing what was described as a routine check.
The union filed the charge in August and announced the move Tuesday, saying the city did not respond to a request made six weeks ago for the material. The recordings and reports are necessary to investigate a possible grievance, the union said.
"They continue to stonewall us, and we're no longer willing to play their childish games," Local 22 president Bill Gault said in a statement. "Clearly the Nutter administration has something to hide, or they would have turned over the information weeks ago."
Mayor Nutter's spokesman, Mark McDonald, would not comment, citing ongoing investigations into the fire, including a federal occupational and safety investigation.
District Attorney Seth Williams also said he would impanel a grand jury to look into the circumstances surrounding the fire, the cause of which has not been determined.
It's likely that the material the union has requested would be considered evidence in the local grand jury and federal queries.
The unfair-labor-practice case would be heard before the Pennsylvania Labor Relations Board.
Contact Troy Graham at 215-854-2730 or firstname.lastname@example.org, or follow on Twitter @troyjgraham.