Wednesday's deposition came just one week before Dolan, considered a possibility to replace Benedict XVI as pope, is to leave for Rome, The New York Times said.
Lawyers questioning Dolan represent hundreds of people who said they were molested by priests in the Archdiocese of Milwaukee, where Dolan was archbishop for seven years before becoming archbishop of New York, the Times reported.
The lawyers were asking when Dolan found about suspected abuse and how quickly he publicized it.
"He has indicated over the past two years that he was eager to cooperate in whatever way he could, and he was looking forward to talking about the good work and progress that took place to ensure the protection of children and pastoral outreach to victims," Joseph Zwilling, spokesman for the Archdiocese of New York, said.
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