Now, as Mr. Ellison runs for attorney general in Minnesota, Ms. Monahan has accused her former boyfriend of emotional abuse and says he once shouted profanities at her, while trying to drag her off a bed.

Mr. Ellison denies abusing Ms. Monahan and said in a statement after the allegations emerged that he cares “deeply for her well-being.” Democratic Party leaders in Minnesota have asked a lawyer to look into Ms. Monahan’s allegations, but continue to support Mr. Ellison’s bid to become attorney general.

The questions around Mr. Ellison come eight months after Senator Al Franken, another popular progressive leader in Minnesota, resigned amid allegations that he made unwanted sexual advances. Now, Mr. Ellison, a high-profile leader on the left, is fighting for his reputation and facing a tough campaign with an opponent using the abuse allegations against him.

Ms. Monahan’s accusations represent a potentially new chapter in the #MeToo movement in which the allegations against a public figure are not primarily about sexual violence or harassment, but emotional abuse. But the allegations against Mr. Ellison, who declined a request for an interview through a spokesman, are turning into a test among many liberals for where to draw the line between a messy relationship and an emotionally abusive one, and some say they aren’t sure where it is.

“I want to make sure that women are believed,” said Betsy Hodges, a former mayor of Minneapolis who identifies as a survivor of childhood sexual abuse and who used to see Mr. Ellison, 55, and Ms. Monahan, 44, together at political events. “I also want to make sure that we follow a process when we evaluate. A bad breakup is not the same thing as abuse.”