The arbitration hearing before a former federal judge will determine whether the NFL overstepped its authority in modifying Rice's two-game suspension, making it indefinite after video of the running back hitting his wife — then his fiancee — was released by TMZ.
Rice and Janay Rice left the hearing separately about three hours apart after each testified at former U.S. District Judge Barbara S. Jones' office.
"I can trust it's a fair process," said Rice's attorney, Peter Ginsberg.
Two people familiar with the case said there's no timetable for Jones to make her decision, though one person said she has asked the sides to submit closing briefs next week. Both spoke to The Associated Press on condition of anonymity because the arbiter has told the sides not to discuss details of the private hearing.
NFL Commissioner Roger Goodell testified for more than two hours to start the appeal hearing Wednesday, according to one of the sources. Ray and Janay Rice attended the full hearing Wednesday.
The hearing began nearly two months after the former Pro Bowl running back was suspended indefinitely by the NFL and released by the Ravens.
League security chief Jeffery Miller and Ravens general manager Ozzie Newsome also testified in the hearing. Ravens President Dick Cass, who was previously expected to testify, was not asked to take part in the hearing, one of the sources said.
The NFL players' union said in a statement that the hearing was fair and thorough, and thanked NFL owners and officials for agreeing to use a neutral arbiter.
"The collectively bargained rights of all players must be vehemently preserved and we take that obligation seriously," the statement said. "This appeal, presided over by a neutral arbitrator, which included a presentation of all the relevant facts, witness testimony to the truth and cross examination, is the due process that every athlete deserves."
NFL spokesman Brian McCarthy declined comment. "We continue to respect the confidentiality order set weeks ago," he said.
Rice was suspended indefinitely Sept. 8 for violating the NFL's personal conduct policy.
Rice is seeking immediate reinstatement, though it's unlikely a team would sign him this season. Rice has also filed a separate wrongful termination grievance against the Ravens.
Goodell originally suspended the running back for two games. The incident occurred inside an elevator at an Atlantic City casino in February, when Rice and Janay Rice were engaged. The couple married a month later.
The league considered the video made public after the initial suspension to be new evidence, giving Goodell the authority to amend Rice's punishment. But Rice's attorneys are arguing he should not be disciplined twice, citing the collective bargaining agreement.
Rice's side also is arguing that he described details of the incident to Goodell when they met in June. Goodell has called Rice's description "ambiguous" while the player's representatives have maintained he gave exact details.
Rice's attorneys also say the indefinite suspension isn't consistent with other punishments issued by Goodell in the past.
Jones was jointly picked by the commissioner and the players' union to hear the appeal. Though it isn't a criminal case, Jones asked witnesses to testify under oath. Transcripts of the testimony will not be released publicly, one source said.
Rice, a three-time Pro Bowl pick, played in two preseason games for the Ravens this year. His last carry was a 6-yard run against San Francisco on Aug. 7.
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Rob Maaddi can be reached on Twitter at www.twitter.com/ap_robmaaddi