WASHINGTON — Senate investigators are scrutinizing links between Jill Stein, the Green Party’s 2016 presidential nominee, and Russia’s campaign to interfere in the 2016 presidential election, searching for evidence of possible conspiracy.

Senator Richard Burr of North Carolina, the Republican chairman of the Senate Intelligence Committee, said on Monday that the committee was “just starting” to look at Ms. Stein’s campaign along with another campaign, which he declined to name, as it continues its investigation of the Trump campaign. Mr. Burr has previously suggested the committee is looking at aspects of the Clinton campaign.

Democrats have seethed for more than a year at Ms. Stein, whose tens of thousands of votes in Michigan, Wisconsin and Pennsylvania either exceeded or nearly matched Donald J. Trump’s margins of victory in those states, which delivered him the White House. At least in certain quarters, they greeted news of the queries enthusiastically.

Jesse Ferguson, a former Clinton campaign spokesman, said Americans ought to know if a presidential nominee, no matter how minor, had become a Russian asset or was simply boosted in an effort to chip away Democratic votes from Mrs. Clinton.