См. также: давайте вернёмся к делу, давать, давать свидетельские показания на прямом допросе, давать согласие на обыск
If you witness an accident, you make a statement to police, describing what you saw. (Vocabulary.com)
He gave a statement to the police. (Longman Dictionary of Contemporary English)
A federal grand jury has called a number of witnesses to give testimony in the pension-fund case. (Longman Business Dictionary)
