Seconded. Just write your character with regard to what your story needs them to be, and nothing else. Brandon Sanderson talks about the trouble he had writing female characters, back when he tried too hard to make them smart and capable, and ended up making them completely one-dimensional. Focusing too much on what your character
ought to be, rather than what would make for the best story, is just dangerous for you. People are far, far more than their ethnicity, and if you concentrate on that in their characterization too much, then you leave out the things that
really influence character--culture, religion, relationships, situation.
Here are some thoughts, though. As an Asian, did your character grow up in whichever country they're native to, or did they grow up in a more Western society? You might try researching, at least a little, the general culture of their country, the norms and expectations people from there would have experienced, and how their views on life would have been influenced by that, or at least by contact with that kind of culture in their family. You'll get far more useful development for your character that way than by wondering if writing a rule-abiding Asian character is racist!
And now that I've typed that sentence, it sounds
really strange. With the going assumption that you would rather not be racist, does that mean you cannot write
any rule-abiding Asian characters?
[Edit: Here's a tidbit you may already know! In Vietnamese culture, it's actually considered the courteous thing to do to pass things to each other with
both hands instead of simply one--cups, food, any of that. It's supposed to show thoughtfulness, and most of all respect, which is something the Vietnamese culture values greatly, especially respect to older people. It's what they teach to their children. And it's knowing and incorporating that sort of detail which can allow you to quite uncontroversially explore the differences between various cultures. Much more than worrying about any of the weird stereotypes out there!]