What kind of writing sample should I submit to an office (entry-level) involved in local politics?

Answer 1

three page college essay on any subject.
they most likely want to see how you present an argument. and if you use spell check.
good luck.

Answer 2

A Memorandum concerning the resolution of a fictional issue that your boss wanted you to resolve.

Include the fictional issue in the first paragraph, and how you went about resolving the issue in subsequent paragraphs, with a comprehensive conclusion at the end.