The body of 47-year-old Oletha Willingham was discovered in the unit block of Carleton Court in the Wilton Community around 2:30 a.m.
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Officers were called there for a welfare check.
Willingham died under "suspicious circumstances," investigators say.
Officers also say Willingham's 2007 black Ford Edge, with Delaware registration PC71928, is missing.
That vehicle may be with a man identified as Lynn "Deszi" Harris. Detectives are working to locate Harris, saying they are concerned for his welfare.
Lynn "Deszi" Harris and the missing Ford Edge
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Anyone with information is asked to contact 302-573-2800.
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