The directories mentioned in the last two posts are almost certainly not free, though - and simply paying somebody to key them in might be a bad idea - depending on your country's copyright laws. In many countries, this would be a copyright violation, and these directories have intentional mistakes to identify violators.
The subject has been discussed here before (do a search for "yellow pages") and the consensus seems to be that in the U.S. at least, yellow pages aren't protected. But is a specialized directory the same as a general yellow pages directory?
I would think that the more specialized the directory, the more claim they have to copyright protection.
In any case, in the U.S. you are not going to get this data from "the public record".
I guess you could get business names and owners and scan for words in the business name and names of business owners, which might be a close approximation. But getting the data would not be easy - there is no central, national registry of business names.
Incorporated businesses are handled by each of the 50 states.
Assumed names are filed locally - typically at the city or county level.
Neither of the above identify "Asian" businesses as such.