Mayor Bloomberg is expected to call for a second special election in central Brooklyn’s 40th City Council district following the refusal by the district’s newly elected council member, Mathieu Eugene, to cooperate with an investigation into his eligibility to hold that office.

Dr. Eugene, who made history last month as the first Haitianborn candidate elected to the council, said at a press conference in front of City Hall yesterday that he will not take his seat on the council “under this cloud.” Since the election, he has been dogged by allegations that he did not live in the district on Election Day, a requirement to hold office.

“The victory has been covered in a shadow and the will of the people is undermined,” said Dr. Eugene, adding that he plans to run again. “I won’t be able to properly serve the community under these conditions. We will not bog down this body with a lawsuit that challenges its authority. That is not the way I choose to enter elected office.”

Instead, he asked Mr. Bloomberg to call for a new special election, which cost the New York City Board of Elections $380,470 in February and is expected to cost the same the second time around. The earliest it could be held is April 24, a spokeswoman for the Board of Elections, Valerie Vazquez, said. She is not aware of any precedent for such an action, she said.

The council has been investigating Dr. Eugene’s recent residential history to determine whether he lived in the district on Election Day. He was asked to give the council a signed sworn statement confirming he is eligible to hold office. A spokeswoman for Speaker Christine Quinn, Maria Alvarado, said Dr. Eugene did not furnish the statement nor provide proof he is legally qualified to take the seat.

Dr. Eugene has insisted that he moved into a three-bedroom apartment in the district prior to the election, but his campaign officials have refused to show his lease.

Dr. Eugene alluded to the council investigation during his impassioned speech to supporters, saying that never before has a duly elected official been asked to submit to such treatment. He said his historic victory has been shattered by technicalities in a law “we all know is vague and unclear.”

A spokesman for Mr. Bloomberg, John Gallagher, wrote in an e-mail that the mayor will call for a special election once he receives written confirmation from Dr. Eugene that he is not taking the seat he is certified for.

The New York City Board of Elections certified the results of last month’s special election yesterday. After Dr. Eugene’s press conference, a former Assemblyman of southern Staten Island, Vincent Ignizio, was sworn in to his council seat during a cramped but well-attended ceremony in the office of the Republican minority leader, James Oddo.

Ms. Quinn canceled an earlier swearing-in ceremony for the council winners last month and said, through Ms. Alvarado, that no one would be allowed to take office until the election results had been certified.

It is unclear how many of the other nine candidates in District 40’s most recent special election would choose to run again. The New York City Campaign Finance Board gave District 40 candidates $304,244 in public funding during last month’s special election.

The executive director of Citizens Union, Dick Dadey, said election law should to be altered to prevent another special election from being called because a candidate is not qualified to hold office. He said Dr. Eugene ran under false pretenses, yet now has a second chance to win under arcane election law.

“It’s a waste of taxpayers’ money,” Mr. Dadey said. “It raises serious questions about his ability to serve as an honorable public servant if he was not able to meet the residency requirements the first time the election was held.”