The incident took place shortly before 4:30 p.m. along Cheswold Boulevard in the Harmony Woods Development.
Officials say officers attempted to execute a car stop.
Police spokesman Cpl. John Weglarz Sr. says the man fled from a routine traffic stop.
At least one officer opened fire, striking the 32-year-old man in the upper body. .
He managed to drive a few blocks away before crashing into a garage on the 100 block of Melodic.
Medics rushed the man to Christiana Hospital where he was pronounced dead.
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The Associated Press contributed to this report.