So... is Murder Princess finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: August 29, 2007
Manga finished: January 01, 2007
... 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
In the kingdom of Forland, a coup throws the monarchy into chaos when Dr. Akamashi overthrows the king.
Princess Alita, now a fugitive, unexpectedly swaps bodies with a formidable bounty hunter named Falis during her escape.
Alita persuades Falis, along with her loyal companions, to pose as the princess and reclaim the throne.
While Falis's brute strength proves useful in regaining power, Alita must now navigate the political landscape to prevent further turmoil and figure out how to reverse the body swap, ensuring the kingdom's stability in the face of the chaos.