An investigation into the complaint has finished and West Mercia Police has said the matter is now closed.
Detective Inspector Mark Glazzard said: "Following receipt of a complaint in November 2015, a thorough and detailed investigation was conducted into an alleged offence under the Localism Act 2011. This investigation has concluded, and no further action will be taken into this matter."
Mr Barrow, from Trefonen near Oswestry stood down as leader of the Tory-led council and as a councillor for Oswestry South in December.
Neither Mr Barrow nor Shropshire Council were available for comment.