Generally speaking no one may obtain the juvenile criminal records of your son unless he consents to releasing them. For example, when applying to become an attorney each applicant must agree to release all juvenile records to the state bar examiners.
In this case, it is possible that there will not be any records outside of the municipality. Since your son never went to court it is possible that the only record of the arrest is in the municipality in which the event occurred. However, it is also possible that this arrest will appear on his rap sheet or in the FBI system. Ask the local police how they handled the documentation of the incident and who might be able to obtain that information.
If you want to be sure that there is not a criminal record, go to your local court house and search for your son's name in their criminal system. If no records appear then it is unlikely anyone outside of the municipality has a record of it.