It seems like all kosher Chinese restaurants have this cat-statue thingy in the front:
Is there any Halachic problem with that? I assume not, if they're all kosher-certified; but why not?
I don't think I've ever seen it, but a quick Wikipedia search on Maneki Neko (the title of your image!) reveals that it is some kind of good luck charm. It would definitely seem forbidden for a Jew to use it for that purpose, but I assume most have it there only for the "ambiance" (which might still be problematic, I don't know).
In any event, the kosher certification probably does not cover such issues; it would probably be out of any mashgiach's radar (until he visits mi.yodeya, that is).
It's not any more of a problem than a khamse is at a North African restaurant. It's a siman for good luck, and not avoda zara. It's only problematic if you reject segulot and other superstitions, like the Rambam does. However, I would question what a JAPANESE cat thing is doing in a CHINESE restaurant!