Rodney King and fiancee Cynthia Kelley
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According to sources, the services will be held next Saturday in Hollywood -- but the family hasn't contacted Cynthia since the day after Rodney died ... and doesn't plan to.
We're told Cynthia hasn't made any efforts to make arrangements for Rodney -- so the family doesn't feel the need to reach out.
We're told the family is also still skeptical about Cynthia's story -- that she heard Rodney banging on the window around 5 AM Sunday and then heard him fall in the pool.
The family doesn't believe Rodney drowned on his own because -- as one source put it -- Rodney was always a great swimmer.