A statement from San Ignacio Police says Jeffrey Furgala, who is reported to be from Calgary, was detained in the Savannah area of the town Saturday night for public intoxication.
Police say he was unable to give an address of where he was staying, so was taken into custody "for his own safety."
The statement says officers found Furgala unconscious in his cell next morning with blood in his nose.
Furgala was transported to a community hospital, then to another hospital for surgery, but was pronounced dead on Tuesday.
The commissioner of police has since launched an investigation into the events surrounding his death.
But the website 7Newsbelize.com quotes a police official as saying Furgala caused his own death when he slipped and fell due to drunkenness.
"We have recordings to show that this person was under the influence of alcohol, and he was assisted by two police officers out of the vehicle, into the station, and into the cell block," Supt. Ralph Moody told the website.
"There was no police officer, or no one who caused injuries to that individual, " added Moody, who is the officer in charge of San Ignacio.