The jury was told the defendant claimed the images were taken for work purposes, but they had not been uploaded to police systems.
Judge Dean told the court: “My conclusion is the Crown cannot demonstrate the serious misconduct here, that the evidence is incapable of demonstrating serious misconduct, so the jury could not reach a conclusion so that Mr Connolly was guilty of misconduct in a public office.”
Consequently, he ordered “not guilty” verdicts to be recorded on the fifth day of Connolly’s trial.
The Crown Prosecution Service has until Monday to consider whether to appeal against the judge’s decision.
Connolly was formally dismissed in 2021 by Merseyside Police, who described his behaviour as “deplorable”.
A misconduct hearing was told other images found on his phone were racist, homophobic and mocked disabled people.
Messages also showed he socialised with a known criminal.