Mr Crockett died at his farm on the Coshquin Road, close to the border with Donegal, at about 5 pm on Monday.
The Health and Safety Executive (HSENI) is investigating.
“HSENI is aware of the incident and is making enquires,,” a spokesman said.
“Our thoughts are with the deceased’s family at this tragic time.”
Police said Mr Crockett’s death is not being treated as suspicious.
Sinn Féin MLA Martina Anderson said Mr Crockett’s death has “shocked and saddened” the local community.
“My thoughts are with the family, friends and loved ones of the man who lost his life at this sad and difficult time,” she said.
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