How have the courts interpreted the Miranda rights of a defendant in a murder case?

Appellant was arrested on the morning of March 6, 1995. The police advised him of his rights under Miranda v. Arizona (1966) 384 U.S. 436, 478-479. Appellant stated that he understood them, but that he nonetheless wished to make a statement. He denied any involvement in the crime, denying that he knew the victim or had any reason to be in the vicinity of her home at the time she was killed. The interviewing detectives told appellant that blood samples provided by him while in prison tied him to the crime. Appellant insisted that the evidence must be wrong, expressing concern that the police already had determined that he was the offender. Appellant agreed to take a polygraph examination so as to clear himself from suspicion.