Q. How would you cite a write-up from a government website in APA format?

The APA's website and blog have examples of how to cite information from a government agency.

If it's a report, here are examples from the Publication Manual of the American Psychological Association.

If it's information found on their website, but not a formal document or separate report, you can cite it as you would any other website.  In this case, the government branch or organization would be the author.  Here are pages on citing a website from the Publication Manual of the American Psychological Association.