The jail was placed on lockdown following the incident.
Kent County Undersheriff Jon Hess described the injuries to a construction worker and two Kent County jail trustees as minor.
Both the department construction company officials said all inmates and workers were accounted for.
Construction company Owen-Ames-Kimball Co. said Friday in a statement it was investigating the cause of the accident and had no further information.
Hess said it appears that a cable snapped as the crane was carrying cement.
A garage area where sheriff’s vehicles are kept was damaged. The main jail that houses inmates apparently wasn’t damaged, and Hess said authorities were checking the structural integrity of that building.
The crane that fell has been used for seven months on a $27 million renovation project, Hess said.