The closure is expected to be permanent, said owner John Riley in a letter to the Connecticut Rapid Response Team.
The company employs 95 delivery diverse, Riley said.
Sheffield Express made many deliveries for Amazon - the online retail giant has been trimming back on delivery drivers after expanding during the holiday season and start of the COVID-19 pandemic.
In July, another Bristol distributor, Systemized Logistics announced that Amazon had cut ties with the company and it would be laying off 50 employees.
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