Similar to Complaint in Criminal Law, in Civil Law it is called Plaint. The Plaint would contain Court name, name, residential address of the Plaintiff and the Defendant and averments [allegation] of committing wrong by the Defendant are elaborately discussed in it.
In fact, as in Criminal Law, Complaint sets in motion the Criminal Case against the Accused, in Civil Laws, the Plaint is the first step towards enlightening the Court the purpose or objective behind instituting the Suit and remedy sought therein.
Order VII of Code of Civil Procedure deals with Plaint.