So... is Mayo Chiki! finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 30, 2011
Manga finished: November 27, 2013
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
Kinjirou Sakamachi is a high school student plagued by gynophobia, a severe fear of women, triggered by physical contact.
His already complicated life takes an unexpected turn when he accidentally discovers a shocking secret about Subaru Konoe, the popular and capable butler of the wealthy and eccentric Kanade Suzutsuki.
This discovery leads to a precarious alliance where Kanade promises to help Kinjirou overcome his gynophobia, but only if he keeps Subaru's secret safe. His normal school life is now turned upside down.
Now, Kinjirou must navigate his crippling fear, protect Subaru's secret, and deal with the often bizarre and unpredictable whims of Kanade, all while trying to maintain some semblance of normalcy.