PC Paul Jackson was found to have committed gross misconduct but a disciplinary panel allowed him to keep his job after a four-day hearing.
Allegations that another police officer, PC James Newton, had used excessive force against the boy were found not proven.
Detective Superintendent Matt Baldwin, Head of Professional Standards, said: “Misconduct Hearings are instigated when an officer or member of staff’s actions, are believed to have amounted to gross misconduct.
“The facts of the incident are presented to a panel of three, with an independent, legally qualified chair who leads the hearing.
“In this case, the panel found one of the officer’s actions had amounted to gross misconduct, and the Chair determined he should be given a final written warning.
“We had no bearing on the decision reached by the panel and we respect their decision.
"We will always look to hold any officer or member of staff accountable for their actions.
“We always endeavour to thoroughly investigate any incident and we demand the highest standards of professionalism, honesty and integrity from our officers and staff, and we not condone, accept or tolerate excessive force or conduct.”