During his term, President John Quincy Adams appointed him governor of Arkansas, but Burton was not confirmed by the United States Senate.

recounts in Marguerite du Pont Lee's Virginia Ghosts and Others, "Among the historic homes in the old County and town of Halifax, N.C. is "Rocky Hill" the summer residence of Governor Hutchins G. Burton, a distinguished lawyer and statesman of the Revolutionary period, who married a daughter of Willie Jones, the famous Jeffersonian-Republican leader through whose efforts the adoption of the Federal Constitution was defeated in the Hillsboro Convention of North Carolina because it contained no Bill of Rights.

Governor Burton and his family were staying at Rocky Hill in the spring of 1836, when he was called to Texas where he owned a large tract of land.

His wife [Sarah "Sallie" Welsh Jones Burton] had been on a visit and was returning to Rocky Hill about dusk in her carriage driven by her servant William and accompanied by an infant grandchild and a nurse.

Her attention was distracted momentarily by the crying of the child and when she looked again expecting her husband to speak as he approached the carriage both rider and horse had vanished.

On account of the slow mail facilities of the time, Mrs. Burton did not hear of the Governor's death until three weeks after it occurred, and she then learned that he had died at the very hour when the apparition had appeared to her and her carriage driver.