WASHINGTON — Special counsel Robert Mueller is scrutinizing the connections between President Donald Trump’s campaign and the data mining firm Cambridge Analytica, which has come under fierce criticism over reports that it swiped the data of more than 50 million Facebook users to sway elections.

Mueller’s investigators have asked former campaign officials about the Trump campaign’s data operations, particularly about how it collected and utilized voter data in battleground states, according to a person with direct knowledge of the line of inquiry but not authorized to discuss it publicly.

The investigators have also asked some of Trump’s data team, which included analysts at the Republican National Committee, about its relationship with Cambridge Analytica, according to two former campaign officials. The campaign paid the firm just under $6 million for its work in 2016, according to federal records.

Authorities in Britain and the United States are investigating whether Cambridge Analytica may have used data improperly obtained from Facebook to try to influence elections, including the 2016 White House race.

Mueller is leading a criminal probe into whether Trump’s Republican presidential campaign had ties to Russia and whether he may have obstructed justice.

The Trump campaign has distanced itself from the data mining firm, which had been financed by major Republican donors and, for a time, employed Steve Bannon, the conservative provocateur who later became Trump’s campaign chief executive.

Trump turned to Twitter on Thursday to boast about his campaign’s social media efforts compared with those of his Democratic opponent, Hillary Clinton, but it was not clear what prompted the declaration.

“Remember when they were saying, during the campaign, that Donald Trump is giving great speeches and drawing big crowds, but he is spending much less money and not using social media as well as Crooked Hillary’s large and highly sophisticated staff. Well, not saying that anymore!” Trump wrote.

A request for an explanation from the White House was not returned.

The exact role that Cambridge Analytica played for the Trump campaign has remained murky.

Staffers at Cambridge Analytica made several overtures to the Trump campaign before eventually being retained. They first requested a meeting in spring 2015, before the celebrity businessman officially announced his candidacy, according to four former campaign officials who were not authorized to publicly discuss internal operations and spoke on condition of anonymity.

Lawmakers have demanded answers from both Cambridge Analytica and Facebook, as Sen. Mark Warner, the Virginia Democrat who is vice chairman of the Senate Intelligence Committee, declared this week that the blooming scandal was “more evidence that the online political advertising market is essentially the Wild West.”

“Whether it’s allowing Russians to purchase political ads, or extensive micro-targeting based on ill-gotten user data, it’s clear that, left unregulated, this market will continue to be prone to deception and lacking in transparency,” Warner tweeted.