AFSCME District Council 33, however, filed a grievance, which posed the question of whether the city had just cause to fire the employees from their recreation jobs.
The arbitrator looked only at the 10 teachers, one of whom had resigned before the terminations were announced, and not the other positions.
In his May 31 ruling, arbitrator Anthony Visco Jr. sided with D.C. 33, which pointed out that the city knew of the teachers' jobs when they were hired as part-time recreation employees.
City spokesman Mark McDonald said the city was reviewing the decision and declined to comment further.
Kurland, who previously said her department was conducting a citywide probe on double-dipping, said Wednesday that the arbitrator's ruling put a halt to that.
"I can't really go forward without the legal advice of the city solicitor," Kurland said. She said she planned to meet with Solicitor Shelley Smith soon.
City Controller Alan Butkovitz also halted his investigation into the alleged double dipping as a result of Visco's ruling.
"We've withdrawn our investigation into that," said Deputy City Controller Bill Rubin.
When the initial reports on the alleged double dipping came out, Butkovitz launched his own inquiry into the difference between the recreation employees - and the deputy mayors who also hold other titles, such as Alan Greenberger, who earns $164,000 as director of commerce and deputy mayor for economic development, and Richard Negrin, the $171,000-a-year managing director and deputy mayor for administration and coordination.
The Controller's Office was concerned that a managing director who is also a deputy mayor could come back to the city years later and request back pay for the second title, Rubin said.
"In the future, they could say, 'I want my money for my time as managing director?' " Rubin said.
The office was satisfied with the response and documentation that the city solicitor provided, showing that all the deputies who held another title had signed waivers saying they were receiving only one payment.
"They met the burden," Rubin said.