“Policeman” means any person who is a member of the police department of a municipality as defined in Section 3-103 of this Code or of a city subject to Article 5 of this Code, whether paid on a full-time or part-time basis, or of a law enforcement organization within a department or agency of the State, and who is by virtue of such public employment vested by law with a primary duty to maintain public order or to make arrests for offenses, whether that duty extends to all offenses or is limited to specific offenses.