The Hamilton County Coroner's Office in Warmbier's home state of Ohio said it will rely on an external examination of the 22-year-old's body and medical records to determine the cause of death.
"It's not uncommon to get autopsy objections,"Justin Weber of the coroner's office told AFP. "It's the family's choice."
Warmbier died Monday of severe brain damage, following 18 months of captivity in North Korea.
He was sentenced in March 2016 to 15 years of hard labor for allegedly stealing a political poster from a North Korean hotel during a tourist trip.
He was medically evacuated in a coma last week, and his death further strained relations between Pyongyang and Washington, with US President Donald Trump calling it a "total disgrace."
US Secretary of State Rex Tillerson warned Monday that Washington holds North Korea "accountable" for Warmbier's fate, and demanded the release of three other Americans held by North Korea.
The coroner's office has reached no conclusions yet as to the cause of Warmbier's death, but his doctors have said that the young man suffered extensive tissue loss in all regions of his brain, likely due to cardiopulmonary arrest.
Medical tests did not reveal what precipitated Warmbier's injuries, but also found no evidence of the botulism infection that North Korea claimed as the cause along with a sleeping pill.
Warmbier will be buried Thursday at Oak Hill Cemetery in Cincinnati, following a funeral service at Wyoming High School, where he attended school and graduated in 2013.
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