Moeller, 51, was being investigated for an alleged assault of a woman who called 911 on Sept. 5 and said she was his fiancée. In the 911 call, the woman said Moeller tried to "strangle" her.
The Browns said in a statement Wednesday that Moeller's suspension "remains indefinite.'' The team said it would have no further comment on the matter.
Moeller is expected to meet with the NFL next week and, although he won't be charged, he could face discipline from the league because alcohol was involved and he has a history with it, a league source told ESPN's Adam Schefter.
In his decision, Walters wrote that "it is quite clear that an incident of a volatile nature took place between Mr. Moeller and [the accuser] on the evening of the call but what is less clear is the exact nature of the incident and the actions of the two persons involved."
Walters wrote that "it is clear to me that the consumption of alcohol contributed significantly to the incident. According to the reports of the police officers responding to the call, both had been drinking."
Moeller and the accuser went to an Octoberfest festival where both drank beers, Walters wrote. The accuser also told Walters of a "road rage" incident when she and Moeller were leaving the festival in which Moeller yelled out his window at another driver and she was fearful they would be pulled over by police at the event.
Moeller and his accuser had "different versions of the incident in the home which precipitated her departure; with her saying he became suddenly angry at her while she was on the phone with her son, and him saying she became upset as a result of that conversation," Walters wrote.
"She says that in anger, he pushed her with his forearm and she was choked by the action, while he says that she became agitated during the phone call and swept items off a table or counter, and he was attempting to calm her and restrain her from further destructive actions. Both say that the other threw trash from the kitchen trash container 'all over the place' during this time," Walters wrote.
The prosecutor wrote that while the accuser doesn't appear to have a history of alcohol-related problems, Moeller has two DWI convictions on his record "and while these past cases do not have a direct bearing on this particular incident, and are not likely admissible as a part of the presentation of a case in court, having these kinds of arrests in one's background often raises a red flag in looking at these kinds of incidents."
Walters wrote that ultimately he decided not to pursue charges because "beyond a reasonable doubt" is very much in doubt in this incident.
Moeller is in his second season with Cleveland following six with the Ravens. In 2011, Moeller was suspended two games by the NFL and fined $47,000 following a drunken-driving conviction.
Moeller played and coached at Michigan, where his father, Gary, was head coach from 1991-94.
ESPN.com's Pat McManamon and The Associated Press contributed to this report.