State Supreme Court Justice Paul G. Feinman fined the city $5,000 on Tuesday.
Law Department spokeswoman Kate O'Brien Ahlers says the city strongly believes it did not violate any court orders, adding that the city is considering its legal options.
Lawyers for the families wanted copies of all communications concerning the crane from the Buildings Department. They also wanted to prevent the city from conducting tests on the crane outside the presence of the families and their experts, the New York Times reported.
The families are suing the crane company, its owner, the city's Buildings Department and others.
Last month the Manhattan district attorney, Cy Vance, said that New York Crane had taken shortcuts to get the crane back in operation quickly and to save money. “Greed and recklessness, motivated by profit, led to the tragic and unnecessary deaths of the two men,” the Times reported.