Moran was found dead in her home in New Salisbury on Saturday, authorities said.
"A subsequent autopsy revealed that Mrs. Moran likely succumbed to complications of Stage 4 cancer," the statement said.
Standard toxicology tests were performed and the results are pending, the statement said, but no illegal narcotics were found at Moran's residence.
Moran was best-known for her role as Joanie Cunningham, the younger sister of Richie Cunningham, who was played by Ron Howard, a child actor who is now a famed director.
"Such sad sad news ... I'll always choose to remember you on our show making scenes better, getting laughs and lighting up TV screens," Howard wrote on Twitter.
The show aired from 1974 to 1984. It was set in 1950s Milwaukee and was a big hit with a catchy theme song and memorable characters such as The Fonz, played by Henry Winkler.
Moran played the same character in the early 1980s in "Joanie Loves Chachi," a short-lived spinoff with her "Happy Days" co-star Scott Baio continuing his role as Chachi Arcola.
In 2012, Moran was one of the "Happy Days" actors who won money in a settlement with CBS over merchandising payments.
Moran had been the subject of reports that she and her husband were living in a trailer in Indiana since losing her home to foreclosure in California. While other cast members continued to act or direct, acting roles became scarce for Moran.
In 2008, she appeared on VH1's reality show "Celebrity Fit Club."
Moran acknowledged having difficulties finding roles in an interview
with producer James Vallo, with whom she worked on "Not Another B Movie," which IMDB lists as her final film credit.
"There is so much reality [television]," she said. "Then the other shows they do have going on, they just kind of want to stay in [one] type of casting area."
She was hopeful, however.
"Slowly but surely it's coming around, and...bringing us back, people that have been in the business all our lives and doing the shows we did."