The investigating officer believes Oscar Pistorius may be a flight risk.
"We don't want another Dewani," the officer says, referring to Shrien Dewani - the British man accused by a South African court of arranging the murder of his wife on their honeymoon there.
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The firm employs 14,000 people at 25 sites across the country.
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Kate Spade was found dead in her New York City home on June 5.