Boschi was quizzed by prosecutors in Potenza after Economic Development Minister Federica Guidi quit on Thursday over allegations she tweaked the country's 2015 budget to suit her businessman boyfriend, Gianluca Gemelli.
Guidi stepped down hours after it emerged that Gemelli is under investigation for abusing his connection to the government in a suspected bid to help his engineering company win contracts with French oil giant Total.
While neither Guidi or Boschi are under investigation, in a wiretap recording leaked to the press, Guidi is heard telling Gemelli that an amendment to the budget law streamlining the approval process for new oilfields in southern Italy would be approved.
The amendment was then signed by Boschi.
Prime Minister Matteo Renzi, who on Monday called for the judiciary to investigate and reach a verdict on the oil project “as soon as possible”, said the amendment was his and that he was willing to be questioned.
Italian opposition parties are seeking to bring down the government over the scandal, with the centre-right Forza Italia party, led by former prime minister Silvio Berlusconi, joining forces with the anti-immigrant Northern League to draw up the motion of no-confidence for both the upper and lower houses of parliament to consider.
The anti-establishment Five Star movement (M5S) also filed its own motion on Tuesday.
"We all have to show we want to send Renzi packing. We will vote for no-confidence," said Five Star member Luigi di Mario, deputy head of the lower house of parliament.
But a defiant Renzi has played down any threat to his government.
"And so they present the umpteenth no-confidence motion. We will go to parliament, I hope as soon as possible," he said on his website, having refused calls on Friday to step down.
The 41-year old prime minister also said his centre-left Democratic Party (PD) was going to sue Beppe Grillo, former comedian and founder of the Five Star party, for saying everyone in the party had "their hands dirty with oil and money".
"We can be unpleasant or arrogant. But we are honest people," Renzi said.
Opposition leaders have seized on Guidi's resignation as fresh evidence that Renzi's administration is every bit as prone to sleaze as its predecessors.
Guidi's resignation came almost exactly a year after then transport minister Maurizio Lupi resigned after it emerged a businessman embroiled in a major public works corruption scandal had given Lupi's son a €10,000 Rolex watch.
While Renzi continues to enjoy good approval ratings and has won plaudits for pushing through reforms in the two years since he seized power in an internal party coup, he faces a potentially tricky test at local elections expected in June.
He has also staked his reputation and political career on a contentious referendum over constitutional reform, scheduled for the autumn, which promises to be bitterly contested.