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)

In legal terminology, a complaint is any formal legal document that sets out the facts and legal reasons (see: cause of action) that the filing party or parties (the plaintiff(s)) believes are sufficient to support a claim against the party or parties against whom the claim is brought (the defendant(s)) that entitles the plaintiff(s) to a remedy (either money damages or injunctive relief). For example, the Federal Rules of Civil Procedure (FRCP) that govern civil litigation in United States courts provide that a civil action is commenced with the filing or service of a pleading called a complaint. Civil court rules in states that have incorporated the Federal Rules of Civil Procedure use the same term for the same pleading. (Wikipedia)

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)

Particulars of claim. Formerly known as a statement of claim. Under the Civil Procedure Rules, a document setting out the case of the claimant and specifying the facts relied upon. The particulars of claim are either contained in the claim form or served on the defendant with the claim form (or within a specified period). (Practical Law Glossary)