I put race when it's integral to the story you're telling in the script/pilot. One script I've written involves dealing with the persecution of being a specific minority in a professional sport, so that character is specified as being Native American in his character description. Another pilot I'm working on involves a family dealing with one member's mental illness, and I haven't assigned any race to them, as I could see them being black, white, Asian, Hispanic, etc...
If you do envision specific races for your characters, I'd take a second to ask why that is. Is it inherent to your story? If so, consider ways that you can highlight whatever it is you want to say about their ethnicity and cultural background in the plot and dialogue. If you just introduce someone as SAM (25, South Korean) and then have nothing in the script that has to do with his heritage, then odds are it'd get changed by a producer/casting director later on. However, if you were to write something like "Black-ish", it'd be pretty damn hard to change those characters to Caucasian without completely changing the show.