Jairam Samaroo, 48, of Rodney Road, Endeavour died at the scene.
Officers were contacted by a contractor who told them that Samaroo was conducting electrical work on a two storey building at Mt Pleasant Road.
The contractor told police that Samaroo was walking on a concrete ramp when he slipped off and hit his head as he fell.
His co-workers went to his assistance and contacted authorities.
Paramedics attempted to revive Samaroo but were unsuccessful.
An autopsy was expected to be performed at the Forensics Sciences Centre, Federation Park yesterday.
TRINIDAD Y TOBAGO: Worker tumbles off building, dies
Con InformaciÃ³n de Trinidad Express
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