Cole later apologised to the intern, and Chelsea, for the incident although a Surrey police spokesman has confirmed that no firearms legislations have been broken as a result of the England defender's actions.
"Surrey police officers have carried out inquiries with Chelsea Football Club and are satisfied that no breaches of firearms legislation have occurred in relation to the possession and use of air weapons," said a spokesman for Surrey police, according to the Guardian.
"The incident took place within a building on private property and those involved were over the age of 18 and did not require any licence to purchase or hire an air weapon or ammunition."
Chelsea have maintained that they would be dealing with the matter internally although Surrey police have confirmed they have offered "strong words of advice" to the Blues.
"Surrey police would like to stress that no allegations of any crime have been made in connection with this incident and that inquiries were commenced directly as a result of the matter being reported in the media a week after the incident occurred," the spokesman added.
"Surrey police officers have visited Chelsea Football Club's training facilities in Cobham and given the club strong words of advice regarding the incident and in relation to security procedures at the training ground to prevent similar incidents taking place in the future.
"There is a code of practice regarding air weapons and owners are advised to follow a number of commonsense rules to ensure the safe handling and storage of air weapons."