The battle over sexual assault allegations against Supreme Court nominee Brett Kavanaugh has spilled into the nation’s contested governor’s races.

Republican governors seeking re-election in Maryland, Massachusetts, New Hampshire and elsewhere are calling for a full investigation of sexual misconduct allegations about him before the U.S. Senate votes on his confirmation.

The calls came as Kavanaugh and accuser Christine Blasey Ford testified Thursday before the Senate Judiciary Committee.

Some of their Democratic challengers are saying they should go even further and call on President Donald Trump to withdraw the nomination or for senators to vote down the confirmation.

Some Republicans have declined to comment, saying it’s a federal issue.

Governors don’t have an official say in the matter, but their words could add pressure in the process.

In New Mexico, where two members of Congress are running for governor, Republican candidate Steve Pearce said in a statement that “it will be up to the U.S. Senate and the American people to decide the path forward.”

Democratic candidate and Congresswoman Michelle Lujan Grisham said she was inspired by Ford’s courage.

She said in a statement that Kavanaugh’s nomination must be withdrawn immediately, citing President Trump’s “refusal to call for a thorough, independent FBI investigation into the multiple credible allegations” against the Supreme Court nominee.

Massachusetts Gov. Charlie Baker told reporters, “I believe Professor Ford.”

Other Republican governors to speak out included Larry Hogan in Maryland, John Kasich in Ohio and Phil Scott in Vermont.