The FAA said the Piper PA 34 aircraft went down on East Main Street in East Hartford near the Connecticut River at about 3:40 p.m.
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"The aircraft was on final approach to Runway 20 at Hartford-Brainard Airport," the FAA said in a statement.
Telephone poles and wires were knocked down in the crash, leaving about 500 without power.
Some roads in the area have been closed while police investigate.
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The Hartford Courant reports that the plane took off from Hartford's Brainard Airport on Tuesday with a student pilot and an instructor on board. They were attempting to land at Brainard when the plane struck a utility pole in East Hartford and crashed.
Police say the plane's pilot was taken to a hospital with serious burns and that the passenger was still in the wreckage and presumed dead. Police did not identify either person.
Two people who were in a minivan near the crash were also taken to a hospital but were not injured.
Officials from the Federal Aviation Administration arrived to investigate.
(The Associated Press contributed to this report.)