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Two recent anime shows from Spring season 2015 had catgirls as main characters (both in the lower row of the following picture).
Etotama, a supernatural battle comedy show, features Nyaa-tan (left lower character), the etomusume of the cat clan trying to become part of the Chinese Zodiac. For that, she must defeat the 12 etoshin (the female representation of the chinese zodiac animals - rat, dog, monkey, tiger, dragon, sheep and so on) to get their seals and prove her worth. It is an original anime based on very old little figurines.
Show By Rock!! is a music anime where the main character Cyan Hijirikawa (lower right) is transported into another dimension called the Sound Cosmos, where its inhabitants are all little animal people who love music in all its forms. There, she joins a band of other animal-eared girls and has whimsical musical adventures with them. It is an adaption of a music rhythm mobile game named "Show By Rock!! Gonna be a Music Millionaire".
Both shows feature CGI for their main attraction (CGI battles for Etotama where characters turn into chibis, and CGI band concerts for Show By Rock!! where the characters turn into cute Sanrio-style animal people). This might turn you off. However, the CGI in both series is of very high quality and top-notch.
Show By Rock!! itself is currently having a short anime airing in this very Summer season (the first episode of the short anime named "Show By Rock!! Short!!" aired last Monday), and will have a second season airing in October 2016.
There are also older nekomimi shows, like the older show "All Purpose Cultural Cat Girl Nuku Nuku".
Another anime show that does feature an android catgirl (or gynoid in that case) in a main role is Pandora in the Crimson Shell: Ghost Urn, which aired in the Winter season 2015/2016. In it, cyborg girl Nene Korobi travels to the island nation of Cenancle Island and meets the crazy scientist Urzal Delilah and her robot assistant Clarion, who is shaped like a catgirl.
