A quiet, reserved person is demure. Its second syllable begins with a kittenish “mew”: “de-MYURE.”
The verb demur has several meanings, but is now used in a sense derived from law to describe the action of someone who resists acting as requested or answering a question. Its second syllable sounds like the “mur” in “murmur”: “duh-MURR.” Note that it is not spelled with a final E. It is used mainly in legal contexts and in journalism, and is unfamiliar enough to many people that they mix it up with the adjective demure. An example of correct use: “If they ask me to make Danish pastries again, I’m going to demur.” Demurs are usually mild, not loud, vehement refusals.