How to Transport a Body Across State Lines

You may have read about the Oklahoma couple who covered up the death of a daughter and who transported that child’s body across six state lines about six times for a total of 1,900 miles before they were caught. While cases like this occur occasionally, body transportation must exist to return a body to a family or to send the deceased to a burial location outside the place of death, among other legitimate reasons. Can you deliver a body yourself, or do regulations exist to prevent this measure?