It was reported last week how 21-year-old Tom Cowan was given treatment over a 48-hour period for a leg wound.
Cole was apparently unaware that the .22 air rifle was loaded.
However, police sources have said that officers are ?highly unlikely? to pursue investigations.
Neither Cowan nor the club reported the incident and Cowan says he has no plans to press charges.
Some commentators had suggested that Cole could be charged with actual bodily harm, an offence which carries a maximum penalty of five years? imprisonment and an unlimited fine.
BASC?s director of firearms, Bill Harriman, said he was not surprised by the decision: ?If the police charged everyone who had an accident, then the shooting community would be in dire straits.?
?It appears there was no intent on Mr Cole?s part ? he was simply behaving in a stupid manner with an airgun, so he?s no different from someone who is unfortunate enough to trip over while out shooting and shoots someone. Not for one minute did I ever think he had committed a criminal offence.?