I've removed the 1981 release dates that were presumably sourced from IMDb (where they're annotated as 'rough cuts').

https://www.imdb.com/title/tt0084445/releaseinfo

The August 1981 screening was for exhibitors, it wasn't a public screening. I think it's safe to assume the March date listed on IMDb, if legitimate, was something similar, though I can't find any source to support it.

https://www.nytimes.com/1981/08/26/movies/embattled-coppola-plunges-into-tv.html

"An unfinished work print of the movie was somehow shown to a group of exhibitors in San Francisco ... No one at Paramount, the studio that is distributing ''One From the Heart,'' would comment officially on why an unfinished print of a $23-million movie - without proper color or sound - would be shown to a large group of exhibitors. It appeared, however, that theater owners from Oregon, which has passed a law forbidding blind bidding, were being shown the film, as is customary in San Francisco, and, as a courtesy, theater owners from Northern California were allowed into the screening."