Ms. de Blasio declined to comment.

Mr. de Blasio’s wife, Chirlane McCray, was present when members of the protection unit used a city police van to move some of the couple’s daughter’s belongings last August, the mayor’s spokeswoman and police officials admitted on Monday.

“Chiara did the majority of the move on her own by subway, but her mother helped with the last few boxes — something many parents do,” said Freddi Goldstein, the mayor’s press secretary. “Members of the family’s detail were standing by and offered to help. Their involvement was strictly voluntary.”

The items moved by the detail included a rolled-up futon mattress but no heavy furniture, according to Ms. Goldstein.

The New York Daily News reported about the move on Sunday.

Michael J. Palladino, the president of the Detectives’ Endowment Association, which represents many of the officers in the detail, said that helping a family member of the mayor move out of her apartment would be outside of the job description for a detective.

“It’s definitely not something that the union would sanction because it’s out of the job title and it’s at the expense of the detective and the taxpayer,” Mr. Palladino said.

Phil Walzak, the top police spokesman, suggested that lending a hand in this case may have been the simpler solution for the officers involved. Had Ms. de Blasio hired her own mover, that person would have had to be vetted with a full background check before being allowed into Gracie Mansion, Mr. Walzak said. And members of the security detail would have accompanied her during the move.