According to the police report, which was recently released, the Two and a Half Men star, 44, claims Mueller flew into a jealous rage over his relationship with one of his daughters after learning the two shared "an affinity for both astronomy and the song 'Drops of Jupiter' from the band Train."
Sheen explained to authorities that he had purchased two tracking telescopes, one for the daughter with ex-wife Denise Richards and one for himself "so they could both look at the same point in the universe at the same time, as a way of staying connected."
An upset Mueller then allegedly said to him, " 'You have a song [that] you share with your daughter, but not one with me?' " Sheen told the arresting officer, adding that the couple's argument escalated and they started to slap "each other's hands or wrists."
A source tells PEOPLE that jealousy over his kids with Denise Richards was sometimes an issue between Sheen and Mueller.
"From the beginning, Brooke had been jealous of Denise having children, when [Brooke] desperately wanted her own with Charlie," a source tells PEOPLE. "After having twin [sons], the differences between Brooke's interests and Charlie's grew enormous, and she would get more upset at the time he spent with his other children or just by himself at his computer."
After their fight, Sheen was arrested on domestic violence charges and booked for second-degree assault, menacing and criminal mischief after Mueller told police Sheen had pinned her down and threatened her with a knife.
He pleaded guilty to a misdemeanor assault charge last week and was ordered to 30 days in rehab as part of a plea deal.
TMZ first broke the news about the contents of the police report.