E! Online said Sheriff's spokesman Steve Schular cited paperwork filed by Hayes's family doctor when he released a statement announcing the cause of the singer and actor's death.
Hayes was discovered Sunday lying unconscious near a treadmill in his Memphis home and was declared dead a short time later. He was 65.
"The Hayes family is comfortable with Dr. Kraus's recommendation to not conduct an autopsy," E! Online quoted Schular as saying.
Hayes's family announced Tuesday that a public memorial service is to be Monday morning at Hope Presbyterian Church in Cordova, Tenn., the entertainment news Web site reported.
"We are overwhelmed with the outpouring of support and love from Isaac's dear friends, colleagues and fans from every corner of the world, and we thank each and every one of them for their kind thoughts and prayer," his family said in a statement. "While he was an iconic figure to many, to us he was husband, father and friend. We will ever miss his love, wisdom, humor and the familiar comfort of his voice."