The government has asked the Serious Fraud Office to investigate G4S for overcharging on contracts to tag offenders electronically.The Cabinet Office will also review all contracts held by G4S and rival outsourcer Serco after an audit found they had charged tens of millions of pounds to tag people who were in prison, dead or had never been tagged.Justice Secretary Chris Grayling told the House of Commons he had referred G4S after the security outsourcing company refused to cooperate with an audit of its billing practices and to withdraw as a bidder for the next round of tagging contracts.Grayling said: "At this time I do not have evidence of dishonesty by G4S but I have invited the Serious Fraud Office to investigate that."He said G4S and Serco had overcharged for the existing £700m contract, billing for undelivered services going back to 2005 at the latest and possibly to 1999.The news is a further blow to G4S after its disastrous failure to supply agreed security services for the London Olympics. Its security guards were also found by an inquest on July 9th to have killed a deportee unlawfully when restraining him.Serco agreed to the audit of its contracts and to withdraw from bidding for the £1.0bn-plus tagging contracts.G4S shares were down 3.8% to 217p at 14:12. Serco was down 5.9% at 640.5p. Both companies are among the government's biggest suppliers.