The couple had been married seven years when they both filed for divorce in 2011, but the divorce wasn't final until 2018, AP reported.
When Rich bought the winning ticket in 2013, they were living separately while the arbitrator worked out the details of their split, including child support payments and custody of their three kids.
After taxes and deductions, the winnings totalled US$38,873,628, according the court filing.
Months after Rich's big win, the arbitrator noted the father hadn't paid child support.
The court also noted that in the years they were together, Mary earned roughly three times as much from her job than Rich did from the business he ran, a T-shirt shop, according to his Bassett's oral arguments.
It took Rich more than a month to realise he had hit the jackpot.
In a winner's profile on the Mega Millions website, he said he had left the winning ticket in his wallet while going on a vacation and a few golfing trips.
"That would have been a terrible time to lose your wallet," the website quoted him as saying.
He said he had played the lottery for years and liked trying his luck on roulette at the casino, and despite the windfall said he intended to keep playing the lottery.
After filing for divorce, the couple agreed to appoint arbitrator John Mills "to decide all contested issues", according to the court filing.
But Mills died in 2014, after deciding that the lottery winnings were part of the marital estate but before the arbitration process was complete.
"As losses throughout the marriage were shared jointly," Mills said per the court filing, "so should winnings be shared jointly."
Rich asked the court to vacate Mills' decision, arguing the arbitrator was biased against him and that "death was the ultimate disqualification", as Bassett said in oral arguments.
The appeals court ultimately decided the case based on the narrower question of whether Mills had made a legal error, ruling that his decision should stand.
In a statement to People, Bassett said his client had already filed a motion asking the court to reconsider its decision, and if it is denied they intend to appeal the decision to the Michigan Supreme Court.