Русско-англо-русский юридический словарь

The legal document which carries a claim is often called a Statement of Claim in English law, or a Complaint in U.S. federal practice and in many U.S. states. (Wikipedia)

Statement of Claim Definition: The document which sets out the plaintiff's allegations of fact and thus, engages the judicial process by seeking trial. A written statement of the initiating litigant, called a plaintiff, in which he/she must state their case: the facts on which they intend to rely upon and the relief they seek, to the defendant and for the public record, for which they seek a civil trial and judicial determination. (Duhaime's Law Dictionary)

complaint (US)/statement of claim (UK) – the written statement of the case made by the plaintiff at the beginning of a civil action (English As a Legal Language By Christine Rossini)

Statement of Defence Definition: A defendant's written answer or reply to a statement of claim, admitting or denying each and every one of the facts contained in the statement of claim and alleging such facts as the defendant wishes to assert at trial in opposition to the plaintiff's case. (Duhaime's Law Dictionary)