So... is Crying Freeman finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: February 25, 1994
Manga finished: April 18, 1988
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Crying Freeman tells the story of Yo Hinomura, a Japanese artist whose life is irrevocably altered when he's forced into becoming an assassin for a powerful Chinese mafia organization.
He's transformed into a highly skilled and efficient killer, known as "Crying Freeman" because he weeps after each assassination, showing remorse for his actions.
The anime explores Yo's struggle with his new identity and the consequences of being a weapon for a ruthless criminal empire, all while navigating the dangerous world of international crime syndicates.