LITTLE ROCK — The Arkansas Supreme Court on Thursday upheld the conviction of a man who was sentenced in Benton County Circuit Court to death for killing a 6-year-old girl.

According to prosecutors at his trial, on the night of Nov. 19, 2012, Zachary Holly entered the home where the girl, identified in court papers as J.B., was sleeping, woke her, picked her up and took her to a nearby vacant house, where he raped her and then tied her pants around her neck and strangled her.

Holly received a death sentence for capital murder, two life sentences for rape and kidnapping, and a 20-year sentence for residential burglary.

On appeal, Holly, now 32, argued that the trial judge should have dismissed the burglary charge, should not have allowed a confession Holly made to police to be admitted as evidence, and should have allowed jurors to be told that Holly had offered to plead guilty to capital murder.

Holly claimed he had a key to the home because he and his wife often babysat J.B. and that he entered through an unlocked door. He said he had authority to enter the home and that he entered looking for medicine for an upset stomach and not with intent to commit a felony, so the charge of residential burglary did not apply.

“This argument is not persuasive,” the Supreme Court said Thursday in an opinion written by Judge Josephine Hart.

The court said J.B.’s mother testified that she had given Holly’s wife permission to enter the home when she needed medicine but did not testify that she had extended the same authority to Holly. The court said it would not consider Holly’s claim that he entered the home without intent to commit a felony because Holly did not make that argument during his trial.

Holly also claimed that at the urging of police, his wife, Amanda Holly, coerced him into talking to police, which he argued amounted to the police improperly using a proxy to elicit a confession after he had asked for a lawyer.

The Supreme Court said testimony at the trial showed Amanda Holly did urge her husband to talk to police and submit to a polygraph test, but she did so for her own reasons, believing he was innocent and should “clear his name.”

Holly further claimed that during the penalty phase of the trial, jurors should have been allowed to hear that he had offered to plead guilty to capital murder. Jurors could have seen this as a sign that he accepted responsibility for his crime and considered it a mitigating factor, he argued.

The Supreme Court disagreed.

“Proof that Holly offered to plead guilty in exchange for a lesser sanction is not evidence that Holly was taking responsibility for his crime,” Hart wrote in the opinion.

Justice Rhonda Wood wrote in a separate opinion that she concurred in the decision to uphold Holly’s conviction but found it “troubling” that Holly — who claimed to read at a third-grade level — received two mental evaluations, but only the first evaluation was entered into the record. All that is in the record regarding the second evaluation is a statement by a lawyer for Holly that he was fit to proceed, Wood noted.

Wood said she hopes the issue will be fully developed and resolved in future proceedings on the question of whether Holly had adequate counsel.