Q141. "When do you refer to the Constitution with a capital C and when do you refer to it with a small C?"
A. Ah, an English usage question — I don't get many of those.
Generally, when you're speaking of any specific constitution, you capitalize the word: the U.S. Constitution; the Vermont Constitution; the Iraq Constitution. If you're writing a paper about the U.S. Constitution, it would be proper to refer to it as "the Constitution" in the text. If you're speaking of constitutions generally, as I have done a couple of times in this paragraph already, you would use the lowercase word.
The confusion can come in when you are talking about a specific constitution in a mix of specific and general terms. For example: "The Framers met in Philadelphia to craft the Constitution." or "The Framers met in Philadelphia to craft a constitution." Using "the" versus "a" changes which word you would use.
Other words based on "constitution" should always be lowercase, such as "constitutional" or "constitutionality."