This month, The New York Times uncovered myriad instances in which people listed as campaign donors said that they had never given Mr. Liu money, or that money had been given in their names by an employer or other Liu supporter. In some cases, people listed as donors could not be located.
The Times also reported that the handwriting on several checks from different donors were remarkably similar, raising the question of whether one person prepared multiple checks.
After the report in The Times was published, a businesswoman in Queens, speaking on the condition of anonymity for fear of upsetting Mr. Liu or his supporters, contacted the newspaper to say that after she declined to give a donation to a Liu volunteer, the volunteer asked whether she would permit someone else to donate in her name.
Mr. Liu, a Democrat who is considering a run for mayor in 2013, vowed to conduct an internal investigation after the newspaper report. He initially brushed aside suggestions, however, that he ask an outsider to help, saying that such a process might be too costly. But he he evidently changed his mind and appointed Mr. Abrams.
In a statement released Friday by Mr. Liu’s campaign, the comptroller said that he expected the investigation by Mr. Abrams to take 60 days.
“I look forward to a thorough and prompt review,” he said.
Mr. Abrams, 73, served as the state’s attorney general under Gov. Mario M. Cuomo and is a longtime fixture in Democratic politics. He has been chosen for a variety of boards and commissions by many elected officials, including the current governor, Andrew M. Cuomo; Mayor Michael R. Bloomberg and Attorney General Eric T. Schneiderman.