Lt. Carroll, who works in Yonkers with the New York State Courts, joked with host Alex Trebek that he first tested for the game show 37 years ago.
"Someone finally came to their senses and asked me to come on," Carrol joked.
Carroll went into Final Jeopardy, which was about awards, with a large lead. He won with a total prize of $32,000. He will compete again Thursday.
The City of Yonkers tweeted well wishes for Carroll before the show aired.
"Yonkers very own Lt. Tom Carroll (New York State Courts) will be appearing on @Jeopardy tonight at 7pm. Tune in and cheer Tom on!," the tweet read.
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