Paul didn’t think much of Roman Law, but he appealed to Caesar
Actually he appealed to Roman Law and thus to Caesar - in the interest of the gospel.
And as they bound him with thongs, Paul said unto the centurion that stood by, Is it lawful for you to scourge a man that is a Roman, and uncondemned? When the centurion heard that, he went and told the chief captain, saying, Take heed what thou doest: for this man is a Roman. Then the chief captain came, and said unto him, Tell me, art thou a Roman? He said, Yea. And the chief captain answered, With a great sum obtained I this freedom. And Paul said, But I was free born. Then straightway they departed from him which should have examined him: and the chief captain also was afraid, after he knew that he was a Roman, and because he had bound him. (Acts 22:25-29)
Then said Paul, I stand at Cæsar’s judgment seat, where I ought to be judged: to the Jews have I done no wrong, as thou very well knowest. (Acts 25:10)