Four years ago, though, authorities successfully prosecuted several officials and members of Local 14 and their colleagues at a sister union, Local 15, during two major cases that focused on organized crime figures and led to nearly four dozen guilty pleas. The men admitted crimes including allowing favored construction contractors to flout work rules and bestowing lucrative no-show jobs on accommodating union officials and workers.

Among those who pleaded guilty and cooperated was Mr. Coriasco, one of several witnesses who questioned the qualifications of some union members. Another union official, testifying at the same trial, balked at the other witness’s assertion that many union members were unable to run cranes. In his experience in the five years ending in 2003, he testified, only two or three Local 14 crane operators were unable to operate the cranes when they reported to job sites. In some instances, he noted, these men had received crane licenses, but really spent their days operating other types of heavy equipment.

The safety of crane operations did not figure in that case, and no one has suggested that operator error played a role in either recent accident.

Still, lapses in the licensing process have been a matter of concern, though typically they have been seen in certifying applicants for some crane licenses, ones that are less advanced than the license required to operate tower cranes.

City records show that more than half a dozen members of Locals 14 and 15 who pleaded guilty to the federal charges still hold such lesser crane licenses. Tony Sclafani, a Buildings Department spokesman, said that a felony conviction, even one related to the construction industry, does not automatically disqualify an applicant.

Those men were able to renew their licenses at least once since their felony convictions. Among them is Lawrence Persico, the son of Carmine Persico, the Colombo crime family boss. The younger Mr. Persico, who pleaded guilty in 2004 to collecting more than $750,000 in no-show jobs, is now out of prison and still holds a Class A crane license.

How and when so many people with questionable backgrounds secured crane licenses remains unclear. One F.B.I. report from 2003 suggests that union members were able to obtain the city licensing test and answers, although the report does not say when.