Lawyers have a terrible habit of Overusing Capitalization. This goes for pleadings, discovery requests, briefs, you name it. Exuberant capitalization is the “cop talk” of legal writing.
Litigators capitalize some other words, like Plaintiff and Defendant, by convention, but many get carried away.
Capitalize the name of a document only when you are referring to a specific document. “complaint,” “counterclaim,” “third-party complaint,” and similar terms are sufficiently generic that you never need to capitalize them.
For any delicate questions of capitalization, as well as other fine points of legal style, Bryan Garner’s Redbook is an excellent legal writer’s reference.