An arbitrator on Friday overturned the National Football League’s indefinite suspension of Ray Rice, the former Baltimore Ravens running back who knocked out his fiancée in an elevator altercation. The decision called the penalty “arbitrary” and in conflict with the facts of the case.

Barbara S. Jones, a former federal judge, heard Mr. Rice’s appeal in a two-day session this month. During those two days, Mr. Rice maintained that he had been penalized twice for the same offense: once when Commissioner Roger Goodell suspended him for two games and fined him about $500,000 as a result of the attack, and again, a few months later, when Mr. Rice was suspended indefinitely after a graphic video of the attack publicly surfaced on the website TMZ.

Mr. Goodell had contended that the video revealed a “starkly different sequence of events” from what Mr. Rice had described in his initial meeting with the commissioner. But Judge Jones concluded that Mr. Rice never misrepresented to Mr. Goodell what occurred and thus did not deserve to be punished a second time.

Judge Jones’s decision is certain to raise fresh questions about Mr. Goodell’s handling of the biggest crisis of his eight-year tenure as commissioner, one that led to a national debate over domestic violence and criticism that the N.F.L., in particular, had been too lax in addressing cases in which players were charged with assaulting women. Mr. Goodell’s initial two-game suspension of Mr. Rice, widely derided as too lenient, was at the heart of the debate.