A Brazilian congressional ethics committee has picked a first-term legislator to lead an investigation into secret Swiss bank accounts allegedly held by Eduardo Cunha, the speaker of the lower house.

The investigation, part of the fallout from a kickback scandal engulfing the state-run oil company Petroleo Brasileiro SA, or Petrobras, could seal the political fate of Cunha, third in the line of presidential succession.

It is therefore a crucial piece of an ongoing political drama surrounding President Dilma Rousseff, currently facing the deepest economic and political crisis in Brazil in decades. As speaker, Cunha is the sole lawmaker with constitutional authority to take up one of the many impeachment requests filed by opponents against her.

Ethics committee members appointed Fausto Pinato, of the Brazilian Republican party (PRB), to lead the investigation and gave him until 24 November to recommend whether the committee should investigate Cunha for lying about the accounts, a breach of conduct that could cost him the speaker’s position and his seat.

The appointment raised eyebrows among some lawmakers because the PRB is a party of evangelical politicians, many of whom have close ties to Cunha, himself an evangelical Christian.

Pinato, 38, vowed to be impartial and told reporters it was “very possible” that he would accept the complaint against Cunha. Aides to Cunha, meanwhile, said the speaker is confident he has enough support on the committee to avoid an unfavourable ruling.

Though charged with upholding ethical standards, the committee itself is controversial in a country where corruption and politics are often inseparable.

One-third of its 21 members are being investigated for alleged crimes – from electoral and tax fraud to money laundering, according to the Estado de S Paulo newspaper. Pinato himself is on trial on charges of giving false testimony in a case that predates his election last year.

“The committee members will try to look good before the Brazilian public. If they give Cunha a free ride, it may become politically costly for them,” said Aline Machado, a political scientist working for the Brazilian congress.

Cunha is under investigation for allegedly receiving a $5m kickback in the massive corruption scandal involving Petrobras.

After Cunha told a previous congressional commission in March that he had no bank accounts abroad, Swiss prosecutors located four accounts in his and his wife’s name at Julius Baer bank and passed the details to Brazilian authorities.