Asobi ni Iku yo!

The short version:

A cute alien girl who looks like a cat-ear cosplayer becomes Earth’s potential ‘First Contact’. Various organizations don’t like this. Hi-jinx ensue.

Blurb from volume 1:

Kakazu Kio, a senior high school student in Okinawa, Japan, woke up to find a strange girl beside him giving off the soft, steady sounds of a person sleeping. Moreover, there are cat ears and a tail growing out of her! In front of the bewildered Kio, his childhood friend appeared carrying breakfast. With a stern voice she asked, “Where is the pretty girl who returned with you yesterday? Introduce me!” Just as these two harsh sentences were about to turn into a full-blown pervert denunciation meeting, the beautiful by-the-books teacher, Itokazu Maki, burst in, making things even harder for Kio. However… this cat-ear girl who calls herself Eris is, in actual fact, an alien! But a mysterious group that refuses to accept this kind of alien contact as well as the CIA, not to mention the Japanese Intelligence Agency, are all reaching out their grubby hands towards the lighthearted Eris! “Stop it! What did Eris ever do to you?!”