The Police Gazette was a newspaper in the UK, Ireland, New Zealand, Tasmania and Australia issued by the police department giving descriptions of crimes and criminals, lists of deserters, etc. Unfortunately I didn't find all to view for free, but they have some at Ancestry and Find My Past. There are digital issues that can be viewed online free at Tasmania Government Archives. UK and Ireland gazettes can be viewed with a subscription to British Newspapers or pay-per-page at Last Chance to Read, who has over 700 issues. You can also go to the National Archives, UK or to other countries' government archives or state libraries.
Some issues of the National Police Gazette, NY published in New York since 1845 can be found online.
Then you have the Police Gazette which was a popular American men's magazine. It published articles with wonderful illustrations about American Boxing and biographies, world sporting events, sports calendars and records, crime stories, and full page Pin-up Girls!
Perhaps you will find one of your ancestors... either on the lam or in the game!