Was the Miranda v Arizona Supreme Court case a criminal or a civil law case?

I understand that he was arrested for rape, but after he was tried and found guilty of the crime he was retried due to the fact that he did not know his rights. Going to the Supreme Court, his lawyers argued that there should be a way for him to have known his rights. Was this case a continuation of the criminal trial or was it a civil trial due to the fact that it was arguing his rights were violated?

This was not a separate civil trial, it was the appeal of the criminal conviction. It was a criminal case.

A girl was missing and the police decided Miranda had killed her. They picked him up and drove around with him in the car questioning him, till he said he wanted a lawyer. After he said that they continued to talk about how the family needed to know if she was dead, till he took them to where the body was.

He was taken to trial, and convicted of the murder. On appeal the issue was the violation of the right to an attorney. The appeal went to the US Supreme Court, along with some other cases, less well known, and we ended up with a judicial mandate for the police to inform people that they have certain rights, and a rule that the confession will not be admissible if the cops violate them.

A really really bad guy got a conviction overturned because the cops forgot there is a constitution.

I foresee similar instances as a result of the present administration's refusal to recognize our constitutional rights.

Criminal....
I am not sure of the particular crime...but he was asked if he wanted to make a statement, without his rights being fully explained, and without him acknowledging a full waiver of his rights.
He confessed...His confession was admitted in evidence. The USSC found that they trial court made reversible error in admitting the evidence, and ordered a retrial without the evidence.

Criminal.
And he was a slimy guy and came to a bad end.

You answered your own question. Since the case was based on the violation of his rights and had made it to the Supreme Court it would be a civil trial.

It was an appeal of the criminal court's verdict.

The case he was incarcerated for was a criminal case. When he sued the state saying his rights were violated, that case was civil.

It was a criminal case in which the police, to extract a confession, gave Miranda a dry run of his hanging. He even appeared in court and showed the rope burns to the judge, who was actually amused at the resourcefulness of the police. The argument, incidentally, was that the whole proceeding was tainted by torture. Of course, this was in the 1970s, when America was still a free country, one that was opposed to torture instead of using it as a matter of course.